Check the toilet float. Post a picture with the cover off.

Might the smell be from the water itself?

Or something near the toilet?

We get that musty smell beginning in Spring when it gets humid so I use Clorox drops in the tank and it works every time.

Here are a few suggestions

Bend the brass wire holding the float up until you get the desired fill level.

We use this for the smell and cleanliness: KaBoom It's not expensive. Might be worth trying. It's a hit here in our niche of the woods.

You might have a small leak under the toilet. I know I've read to never caulk a toilet to the floor because if you get a little leak it will just soak into the floor and not be able to get out where you can see that it's leaking. I've had my plumber just caulk the front half of the toilet for cleanliness.

If you have a small leak, it might not be enough to actual make a puddle outside of the base, but it could be creating a musty smell (or worse).