Yes. Right now. Don't put it off.

After you take down the fibreglass, you can ensure the drying is fast and thorough with rental heaters

Fibreglass is pretty much useless in a garage ceiling with a room above.

So replace it with either tightly fitted layers of foam board XPS (extruded polystyrene) or EPS (expanded polystyrene).

Better yet, spray foam. Or "flash 'n' batt"--spray foam followed by fibrous insulation.

Very confusing write-up. Flooded a bathroom over the garage? Remove flooring in bathroom, remove all ceiling in garage.

Your garage must have a fire separation ceiling of Type X drywall, and the ductwork needs to be encased as well.

Bathroom is more or less over the garage. Garage was built prior to firewall code and thus is currently grandfathered in as far as requiring a fire separation. I've removed most of the insulation from the garage ceiling. Some sections of the insulation are certainly wet, but overall doesn't seem SUPER wet. I plan on also pulling up the vinyl floor in the bathroom to air out under it. Might just be a good time to move forward renovation plans for that bathroom.

Nonsense. First, it is not a "fire wall." It is merely a layer of non-combustible material that provides fire separation between the occupied rooms and the garage, and the requirement has existed long before your house was built. Even if your house was built prior to codes or garages in basements, it would be negligent and criminal for you not to protect your family and screw up a few $8 sheets of 5/8" Type X drywall, now that you know it is important (and required by code).

Minimum is 5/8" on ceiling, 1/2" only on the wall between the garage and house. It would be smart though to follow your local jurisdiction if they have amended it to fully 5/8 on all the walls. You probably have an interior hollow core wood door to the garage too. Might be good to combine some garage stuff with the bathroom remodel.

I know you are just asking about preventing mold, but hey kids are involved.

Addressing the Garage is certainly on the agenda, though I don't believe it's as simple as just screwing up some drywall. I've yet to engage a contractor, but how on earth do you handle all the pipping that is running below the joists? I measure about 83' of clearance between the floor and the bottom of some of those bigger pipes. I'm not sure how such things are usually handled, but It would seem I would have to redo all the plumbing to get sheetrock on the ceiling.

THere's also water leak sensors that will sound an alarm

https://www.amazon.com/s?k=flood+sensor&ref=nb_sb_noss

Rather than re-locate the existing plumbing and HVAC, you may be able to build a drop ceiling beneath most of it. Then attach the X-rated drywall and properly seal all the penetrations using firestop products. That's what I've done in most of our new builds. Alternatively, some services could be re-located above, some left below the finished ceiling.

Full 4x8 sheets don't have to be put up intact. It may involve pieces to slip behind pipes. If some of the smaller EMT conduit is against the joists, you can put furring just the thickness of the pipes then drywall over that, and leave the copper waste below the ceiling.