I very much doubt you have wires running back to the switch from the fan and light separately - normally the wire from the switch (or power depending on how they're wired) would run to the first thing, say the light, then a set of wires would run from the light to the fan - don't assume you can just pull them apart, in fact I can pretty much guarantee you can't - but someone who knows more may disagree - but you have to ascertain what wire goes where.

My downstairs bathroom is the reverse - fan and light are separate, but I'd prefer them together (always the way, isn't it? ) so the fan has to be on. Only light is one above the sink, so my plan is to add a ceiling light and connect that with the fan.

It sounds like you are saying that both the screw and backstab are used on both terminals of the switch.

That suggests that two of the wires (which are on the same terminal) go to the fan and the switch. The other two are the incoming power, and the feed to whatever is downstream.

If that is the case, then take the incoming+downstream wires and wirenut them together along with two pigtails. The pigtails go to your new switches as inputs.

Test the wires first to make sure this is the case.

never assume anything when working with existing wiring, old or new. It's been my experience that many people who install wiring in houses when they are built have a serious drinking problem! You're liable to find almost anything.
Use a meter and find the load side of the switch. on the oposite side remove one wire at a time and determine what stops working. You may have separate wires going to the light and fan. If so then install a double switch and your done. or that extra wire may go to the counter outlet, or to another outlet elsewhere. or it may just go nowhere!

Those 'extra' wires are probably the supply. I doubt very much that it's legal to use the mounting screws AND the backstabs together, although I guess it's a novel way of joining them. Backstabs are legal in most places but not considered good wiring practice. I'm in the process of redoing everything in my house, as the so and so's did EVERYTHING backstab.

Consider this - if you were planning to wire the fan and light together, why on earth would you run the wires from both, all the way back to the switch, rather than running on from one thing to another, which would use way less wire and be way less work.