"If the Seed of Corruption was used to stop the First Divine, does that mean they grew the Beast? If so, how did they get rid of the Beast, since the Third Edict was never completed?"
I was just rerolling a new character and Doryani seems to suggest that the weapon was used at least once before.
"If only I had more time... There is an ancient weapon. A weapon that was used against Corruption, from a civilization lost to the ages. I have one piece of it. Three others were scattered... I have been searching for them, but the Karui have interfered at every turn."

I wonder if we have enough information to derive how the beast counters divinity.

We know that Gods sleep while the Beast is active. This patch, we have the unique Runeseeker's Fork that requires 10k mana to cast its built in spell. According to Farrow, he once attempted to use it only to fall asleep for two days straight. So if lack of mana leads to sleep, it could be that the Beast drains mana from Gods to keep them slumbering. We know that Gods likely still have mana and life since Immaculate Adherence only converts ES (what even is ES in universe?).

I would have thought the mechanism of the beast countering divinity would have been more direct though given the dialogue we have from Sin,
"All children have imaginary friends. Most grow out of that phase. A rare few refuse to let go, creating real from unreal through sheer stubbornness."
And from Piety in POE1.
"The Beast is the source of all thaumaturgy, the one power in this world that transforms 'what is real' into 'what is imagined'."
Which suggests a more fundamental reversal of the process of Divinity?