The UV bulb in your contact printer is designed for UV sensitive materials - not for the printing papers you have listed.

Those papers might respond to the UV light, but it would be hard to make them behave reliably.

And the UV light itself is potentially dangerous to your eyes.

If the bulb is replaceable with something that emits in the visible spectrum, it would probably be better for you.

The contact printer you have might be of interest to photographers who work with alternative processes (e.g. cyanotypes, Van Dyke brown), where the materials are only really sensitive to UV.

Some of your confusion may arise from the fact that it seems common to refer to what I would call a "contact proofing print" or "contact sheet" as a "contact print". As mentioned above, some people use contact printing to make final, exhibition quality prints (usually from large format negatives). Some of those contact prints are made on specialized paper (eg Azo) which is very slow, and therefore not suited to enlarging.

A lot more use a piece of glass, a light source like a bulb or an enlarger, and sheets of photographic enlarging paper to make "contact sheets" which serve as proofs for one or more negatives - frequently an entire roll of film at a time.

In place of the piece of glass, I use a "Custom Negative Proofer" like this one:

I use it with my enlarger as a light source. The combination is quick and simple. Once you determine the exposure (using test strips) for a particular paper, you record the settings on your enlarger (height, focus setting, negative carrier, aperture) and then reset your enlarger to those positions for subsequent contact sheets.

Or if you have something like an enlarging computer (eg Ilford EM10) you can use that and the lens aperture to match light intensities.