Fire Emblem: Fortune's Weave Helps Explain Sothis. Somewhat. (Spoilers)
Spoilers. Obviously. You've been warned.
Did you play Fire Emblem: Three Houses? If not, shame on you. Close this window, play the game at least once, then come back.
Actually, you really should play all four paths (five, if you count Cindered Shadows which is DLC).
Then, you should play Fire Emblem: Three Hopes, which is a musou game (think Dynasty Warriors) but adds even more lore.
This publication focuses on Sothis. That's why you need to play the games.
What IS Sothis?
Sothis is an alien being. No, we're serious.
If you ever played Chrono Trigger...Sothis is basically the same thing as Lavos.

Lavos crash landed into the planet and buried deep into its core. In the "future", Lavos then surfaces and destroys everything. That's what Chrono Trigger's point is: to stop Lavos.
Sothis is basically Lavos: an alien being that crash landed into the planet and burrowed deep into it, then went to sleep.
Sothis left an avatar (simulacrum) as an extension of itself - think of a remote monitoring device - to learn and understand the world. That avatar was the predecessor to child Sothis - described by Fortuna as being in the image of a blind child that had befriended Sothis and passed away; Sothis would then recreate the image of the dead child as the new simulacrum.
That avatar is/was what got killed by Nemesis at Zanado, where the Agarthans took the bones which resulted in the sacred Weapons spread all around. Some of these became the Sword of the Creator.
The creator of the Sword of the Creator, as well as the weapons Nemesis used to kill Sothis' simulacrum, was the Agarthans. Yes, "Those Who Slither In The Dark".
But they weren't just "evil". The Agarthans were / are partially guided by a sentient AI called Vritra. Vritra was in contact with satellites in space watching things at the point Sothis crash landed.
AGARTHA, or rather:
ALLIANCE of the
GREAT
ACOLYTES of
RECONDITE
TECHNOLOGY and
HARMONIC
ALIGNMENT
Was an organization that existed in the distant past, before Sothis crash landed. After impact, they deployed Megaliths (supercomputers) to analyze the UFO and determine what to do. But Vritra automatically deemed it a threat and summoned down attacks from the satellites to try and destroy alien Sothis.
Alien Sothis retaliated by triggering a major flooding event (The Great Undoing) that nearly killed all humanoid life on the planet, but especially the Agarthans.
Sothis' children were then deployed to various parts of the world to replenish the world and its people and guide them (which meant worshipping the progenitor god, Sothis). One of these children: Rhea. Or rather, Seiros.
The anger of the Agarthans seen in Three Houses and Three Hopes is due to revenge for what Sothis had done, levied against the Nabateans (Sothis' children) and all humans who worshipped or supported them.
Fabio - or rather, Anacharsis - was alive during this set of events. Which is why he tried to interact with Megaliths in Dagda to try and determine the current state of Vritra, only to find that the White Egg survivors had put a trap in it designed to eliminate any straggler Agarthans.
How This Connects To Byleth and Edelgard
The Crest of Flames (last held by Byleth) was basically a "piece" of Sothis that the Agarthans stole from the corpse of its simulacrum body when Nemesis killed it.
Seiros's (Rhea's) army confronted Nemesis' army to stop it from rampaging. In the process, Seiros killed Nemesis and took back both the Sword of the Creator and the Crest of Flames along with all of the other Crest Stones that Nemesis had possession of.
Rhea (Seiros) wished to revive her deceased mother (the simulacrum of the progenitor god). To this end, she believed that the Crest of Flames was the key, if it were implanted into another simulacrum. Fortuna mentions that a simulacrum that sits on Sothis' throne (which the Church of Seiros was purposely built on top of to hide and protect it plus the Stones) would immediately absorb the 'soul' of Sothis, becoming the new oversight avatar.
Cindered Shadows reveals that Rhea had tried this with multiple people, creating what was effectively a soulless puppet and implanting the Crest into them; only to have them reject the Crest and die.
Sitri, Byleth's mother, was on the verge of dying, but gave birth to Byleth, then (allegedly) told Rhea to implant the Stone into Byleth to continue the work, which she did. Sitri died, but was hidden deep within Abyss to hide the truth, but also for Rhea to go and see her every so often. The Crest of Flames basically took over Byleth's heart.
Jeralt, the father of Byleth, suspected something was wrong with the child as it wouldn't cry. Thinking Rhea might have done something, he took the child and abandoned his post at the Church, becoming a mercenary and raising Byleth.
Here's where Three Houses and Three Hopes essentially branches off.
Three Houses
As Byleth goes to protect Edelgard from a fatal strike from a thief, the soul of Sothis awakens within them to freeze time, taking the form of child Sothis. Most likely, this is because of the presence of Edelgard's Crests.
Edelgard was born with a minor Crest (the Crest of Seiros). During a political coup triggered by the Agarthans, she was imprisoned, and experiments performed on her. One such experiment resulted in the Crest of Flames being implanted alongside her existing Crest, turning her hair white and giving her inexplicable powers. She would also have a burning hatred for the Crests, because they meant she would not live a full life (Lysithea reveals that the experiment meant a significantly shortened lifespan) or experience what it meant to be human and not dependent on Crests.
Edelgard, as the Flame Emperor, was actually the one who hired the thief to begin with.
Jeralt and Byleth are convinced to return to Garreg Mach with the others, resulting in a reunion with Rhea. Rhea recognizes Jeralt, and suspects the child is the same as the one she implanted the Crest of Flames into years prior.
During a meeting with Rhea, Sothis' name is mentioned for the first time as 'Goddess Sothis', which child Sothis reacts to, realizing what she truly is. For now, she's chosen to protect Byleth but not interfere with them, but wants to understand what happened.
A paralogue has Byleth visiting Zanado, the Red Canyon. This place used to be where the Nabateans lived in peace before Nemesis' army sacked it. It's also where the prior simulacrum was killed and plundered, triggering memories in child Sothis.
Separately, the Agarthans used Heart Core technology to be able to take over deceased bodies and essentially live forever. With these alternate forms they take over key members of the Adrestian Empire and initiate the Insurrection of the Seven, the political coup that results in Edelgard being sent to Faerghus along with her mother.
The Heart Core is an artificial version of what Rhea had done with the Crest of Flames and real bodies - allowing a still body to reanimate as an entirely new being. But they also provide power for a one-time-use spell to send beings into Zahras, which is believed to be an artificially generated world somewhere in one of the Agarthans' subterranean installations.
Solon takes Kronya's Heart Core (Kronya is believed to be an artificial being) and uses the spell to send Byleth to Zahras. Sothis mentions that the only way to escape the void is "the power of a god", meaning her. But doing so means she will no longer be a separate being, she must complete the merge with Byleth, and does so.
When Rhea later convinces Byleth to take the throne (because she thinks the soul will re-enter the simulacrum), nothing happens. This is because Sothis was already awakened and already merged with Byleth; but because she had bonded with him as an individual, Byleth remained in full control of their faculties.
In Crimson Flower's ending, killing The Immaculate One (Rhea) exhausts the Crest of Flames, freeing Byleth's heart so it can live on.
Three Hopes
Shez, a mercenary, intercepts the thieves and kills Kostas (the leader) long before they get a chance to attack Edelgard, Dimitri and Claude. Byleth, the mercenary, overwhelms Shez at first, but Arval (Epimenides) activates to keep Shez alive while trying to go after Byleth, who flees.
Though not known at the time, Epimenides is now the 'soul' of an Agarthan that fought against Seiros, the same war that Nemesis fell in. Epimenides is believed to have died there, but had perfected the art of transferring consciousness to other bodies. Shez is believed to be an artificial body that received Epimenides' soul at some point.
Arval retains the hatred that Epimenides had at what alien Sothis had done to his people. Arval detects the soul of Sothis present in Byleth and briefly takes over Shez to kill them. But Sothis forcibly takes over Byleth's body to avoid being killed and forces Arval/Shez to retreat. Byleth recognizes Arval as one of the Agarthans and decides they must be eliminated.
Sub Summary
Agarthans are pissed at Sothis for wiping their people out; Sothis is pissed at Agarthans for trying to kill her repeatedly.
Three Houses Sothis originally only ever encountered humans, with no reason to want them dead. It wasn't until Solon sent Byleth to Zahras that Sothis' hand was forced.
Three Hopes Sothis encountered an Agarthan that was straightaway trying to kill her (again), causing her to act.
Bottom Line of Sothis
"Sothis" is an alien.
"child Sothis" is a spirit/soul/essence designed to inhabit a simulacrum to eventually represent Sothis topside and watch over the world (adult Sothis).
Edelgard rejecting the teachings of the Church and referring to "false gods" was actually telling the truth without realizing exactly why she was right.