Is a bathroom required by code to have a window or exhaust fan?

Codes differ between areas and across time. The International Residential Code requires SOME form of venting, either a fan exhausting to the outside with at least 50CFM or a window with at least 1-1/2 sq. ft. of opening area. Whether or not your locality adopted those standards at the time your condo was built is not something we can help with. But code or no code, an un-vented bathroom (with a bath or shower) is a bad idea and ESPECIALLY in a humid part of the world.

"Ventless" bathroom fans are only for fart control by blowing the air through a carbon filter, they have zero effect on humidity and the likelihood of mold and mildew formation.

This gets into an interesting discussion as to when something has to be "brought up to code". This might be worth its own question/thread, but I'll put it out here anyway.

In many areas (your mileage may vary), your local jurisdiction/inspector may require that as part of a major remodel of a bathroom or kitchen for example, that the bathroom/kitchen be brought into compliance with the current codes. For a kitchen, this might mean having to provide 2 20-amp GFCI protected circuits for counter outlets, even if there was only a single 15-amp non-GFCI circuit there originally. In a bathroom, it might entail providing the proper venting.

OP says his condo was completely remodeled. To me that means it needed to be brought up to current code requirements, which means having the bathroom properly vented. But being a condo unit, this may not have been practical.

The gray area is what differentiates a minor update from a major renovation. Tearing a bathroom down to the studs is definitely a major reno. Replacing a toilet - no. Painting the room, NO.