Game won't load past title screen and crashes

GoosMonger​  Your saves aren't gone, they're just in the folder you moved.  You can move them to the new Sims 4 folder in Documents > Electronic Arts now and see what happens.  If the game stops working, remove your saves again and put back only an older one, a file that ends in .save but is older than at least one other file that ends in .save.  If that one doesn't work either, remove it and try a different older one.

If your saves do work, you can transfer the contents of Tray as well, plus Screenshots and Recorded Videos if you care about those.  The other files and folders can be discarded.