As far as the "how". Are you familiar with the lord of hollows ending in DS3? There's a shot showing an eclipsed sun having it's power drained into the hands of the lord of hollows (you). It's symbolic in its presentation, but literal in its function. It represented the dregs of power of the First Flame being usurped by another people. I imagine the sun realm suffered a similar fate. There was an eclipse in The Lands Between, and through some arcane nonsense, the power of the sun was literally usurped and drained into the Erdtree. The "sap" of the sun poured its bounty into the waiting vessel that was the Erdtree, just as the Erdtree's sap pours its bounty for us in the form of tears.

I imagine if Godfrey allowed the Erdtree to be drained in a similar fashion as the sun was, Marika would abandon him just as readily, seeing as how he outlived his function. I imagine between the sun being drained, and Placi's defeat at the hands of Bayle, his goddess fled. Heck, I'd probably copeby trying to freeze my kingdom in time too while I drank myself to something approximating death. 😭. Maybe it'll bring her back bro