You have some moisture issues and water intrusion, you need to take all that out, see whats is going on behind there, and redo everything. Also being this low to the ground is not a good idea.

The reduction to 2.5" with a 90º turn renders the exhaust likely useless.

Note here Broan specs no less than a 4" exhaust for bath or ventilation fans.

Laying the pipe on the ground provides convenient access for all sorts of critters.

If the fabricator of the hillbilly venting also installed the bathroom, there will be other problems as well.

By the looks in your pictures, there could be a lot of mold behind the walls. Can you post pictures of the entire bathroom, please.

Definitely more issues than just ventilation.

Your bathroom ventilation looks awful tbh. It shouldn't surprise you that there are some issues with it. You need to change the duct or at least clean it extensively. I had almost the same problem when I got my first apartment. The things were quite bad with the duct system and I needed to repair it. Not only that but I had to clean the tubes. I didn't know how exactly to do that, so I hired professionals in this field. I called the guys from https://epicductcleaning.com.au/duct-cleaning-melton/ and they helped me to clean the duct. Now my ventilation system works perfectly.

Thanks for your help everyone - turns out the drain in the shower (from a kit) was not sealed had come slightly loose, and water was slowly seeping under the shower every time it was on. That, combined with poor ventilation caused the problem.

Good to hear something got fixed!