Visible moisture on all walls?

How long do you run the fan after a shower? You could get a humidistat and see how long you need to run it to reduce it. You could get a humidistat switch which automatically runs until a certain humidity level is reached.

Have you tested the fan's function? They sometimes have blocked dampers - stuck during install.

How many CFM is the fan? It is big so probably adequate but size isn't everything.

You can hire an energy rater to test the fan flow.

The paint is not the issue nor is the fan location (IMO).

I like your contractor's fix. A powerful vent mounted on the ceiling in the shower and immediately ducted to that outside wall will solve your problem.

If dry makeup air is supplied by a door undercut, make sure its large enough.

Bathroom ventilation serves a number of purposes, one of which is to exhaust moisture-laden air. You have a large shower with two shower heads which has the potential to pump a lot of moisture into the air. How much ventilation does your bathroom need? You can consult the guidelines of the Home Ventilation Institute https://www.hvi.org/resources/publications/home-ventilation-guide-articles/how-much-ventilation-do-i-need/

I think you'll find your problem will be solved by installing an appropriately-sized vent fan directly above the shower, ensuring the door undercut is adequate as RES advised and running the vent fan whenever the shower is turned on and for at least 20 minutes afterwards (I'm paranoid about mildew so I run mine for a lot longer.)

With respect to your question about who is responsible, your builder should construct your addition substantially as per the plans and specifications included in your contract.

Have a look and see what they show for the make/model and location of a vent fan. As for repainting the bathroom, condensation on surfaces is not under your builder's control and is not considered a warrantable condition in NAHB's Residential Construction Performance Guidelines.

“And will that make bathroom unable to steam up at all and be too cold to shower in??”

puzzling statement. I don’t want my bathroom to “steam up”. If it steams up, you will probably have the dripping and staining. if you install another fan, do you still think the bathroom should steam up?

With two exhaust fans it might be necessary to install a transfer duct from the bathroom to a hall.

Has your contractor checked to see if the duct is blocked? Kind of crazy, but our bath vent didn’t have an adequate cover on the outside and a bird built a nest and laid babies in our ducting. Took my husband to figure it out and fix it, then we put a better cover over the exit point. The babies survived FYI.

Our previous bath had similar problems with moisture on the walls. We gutted it. We had two combo can lights/vent fans installed in our shower. They do a great job of venting the humid air from the bathroom. The shower is not drafty and we do not get cold while in the shower.

@David Cary,

Au contraire: the location of the vent fan is indeed relevant.

Warm, moist air is less dense (i.e., more buoyant) than dry air. As the warm, moist air produced in the shower rises and moves across the ceiling toward the vent fan, there is a real potential for condensation to occur as the air cools to--or below-- its dewpoint.

Locating the vent fan directly above the shower mitigates the risk of condensation outside the shower's footprint.

Did I say not relevant? I might have. I meant that I didn't think it was the issue.

I have never had a vent directly in the shower footprint and never had an issue like OP. But each situation is different - particularly owner behavior. Last 4 houses had similar shower styles - ie fairly large showers with glass about 2 feet down from the ceiling. Never had this issue.

In my area, I don't think I have ever seen the shower/bath fan in the shower footprint. Can't say that I have made special notice however.

Either way, I think OP (now lost) was concerned about a cold shower stall and a really powerful fan in the footprint could make that happen so wouldn't be the first thing I would try.

I would bet on blocked vent or not running fan long enough. Nearly free things to try first.

What are the cfms of the current fan? We had the drippy walls in one of our bathrooms. Tub/shower combo. Not every wall just the one near the shower/tub. The fan was right next to the shower. Turned out the fan was only 50 cfm. We replaced with higher cfm fan and no more drippy walls.

The HVI guidelines in the link above will indicate the required fan capacity based on the size of the bathroom and number of bath fixtures. I'm guessing the contractor got the fan at the local big box store and that it's rated at 70 cfm or less which would be inadequate for this bathroom if it's 100 SF or more in area. The fan rating should be easy to find after removing the vent fan cover--no need to wrangle wildlife that you suspect might have made their home the duct work if you can find the answer that easily.

Adding a vent fan above the shower should do the trick.

As to the OP's question "Who Messed Up Here?" We still don't know if one or more vent fans were shown in the plans and what, if any, information was listed in the specifications. If the job was competitively bid, the least expensive alternative that meets the code and specs is typically what you get.

I agree, ours was definitely an out of the box situation:) Just put it out there in the event all the rational ideas fail. Our fan is also just outside the shower, also with glass walls that purposely end about one foot down from the ceiling. We had a fan inside our last shower, and it did feel cold, so this was our solution. Aside from the birds, no issues. Hope the OP has solved their issue. If it’s always been this way, unlikely to be birds.