Is it recorded anywhere that it did? You'd think that the sinking of a continent would have a huge impact on another continent that isn't far away, but this is Nirn and our earthly physics don't belong there.

Oh and I'm talking about weather, tidal waves, ect. not the migration of Yokudans/Redguards.

We don't know that it "sunk" exactly. Many people call the disappearance of various lost continents (Aldmeris, Yokuda, Atmora, etc) "Serpent Breaks" and prefer to think that the simply vanished.

Isn't it mentioned in Oblivion that people still set sail to Yokuda? It should probably still exist physically in some shape or form... It's probably just completely [censored] up.

Redguard had a map of it and west Tamriel. It's like 5 remaining islands by now.