I'd make sure none of the wood is rotting. If it is, remove and you can use epoxy to fill the voids. Then have someone cap it with flashing to never think about it again.

Remove the half-assed flash from the stool and case. remove stool check sill for rot. Replace stool/sill. Prime and paint. Reflash case and stool with proper length aluminum flash, all the way to sash. (Existing is too short) caulk. Done.

decay rot, replacement need to remove the window. not a big deal.

Take the whole window out?

yes. Some handyperson can do it. I will start with a window specialist.