Depending on the configuration of your bathroom, a bath vent fan can serve to exhaust moisture, odors or both.

I suggest you keep the vent fan in the toilet area and add one in proximity to the shower to deal with the moisture--each with it's own dedicated exhaust duct to the exterior. I have a timer on mine that runs the exhaust fan in the shower for 30 minutes after a shower to lower the relative humidity in the bathroom. It's not without expense, but it's a preferable alternative to mold.

+1 on leave the toilet room exhaust. That is historically what exhaust was only required for. Now, code has updated wording to include "bathrooms," but doesn't talk about humidity (yet). HVI has more in-depth recommendations for bathroom exhaust and ventilation.

You can only combine ducts if you are pulling the exhaust from 1 attic/roof sourced fan. When you are pushing the exhaust from ceiling sourced fans, you need to keep 2 separate ducts with each their own discharge.

You have options for the shower. Based on the finishes I see in the pic and thus the level of bathroom, a combo recessed light/vent inside the shower footprint might fit well. Or a light inside, with exhaust/heater outside the footprint. With a combo light/exhaust/heater, it will all be moved just outside the shower footprint, so make sure you're fine aesthetically with that next to the old ceiling fan light outlet - I'd guess you will be putting a chandelier there. And don't have the shower light switched to any of the same switches as the chandelier, toilet, or vanity lights.

Are you in California? If so, you cannot add a light on the same switch as the exhaust fan and you must have a humidity sensor on the exhaust fan.

I'll second the recommendation to install a combo bath fan/recessed light in showers. It provides excellent moisture control and it's unobtrusive.

I can't tell the distance from the edge of the tub to the former ceiling fan mount from the photo, but the 2018 International Residential Code, which forms the core of most statewide building codes, (section E4003.11) doesn't permit the installation of cord-connected, chain or cable hung luminaries, lighting tracks, pendants or ceiling-suspended paddle fans in the zone measured 3 ft horizontally and 8 ft vertically from the edge of the tub. Check that before deciding what to install there.

Note the electrical requirements. Examples:

• Panasonic FV-0511VHL1 - requires 120 volt, 20 amp dedicated circuit
• Broan QTX100HL - requies 120 volt, 20 amp dedicated circuit

You may not be able to use the circuit that was used for the fan. That may be a 15-amp circuit and one shared with outlets and other lights.