If your water report was "not hard" then I would look to other sources for your issues with your shower. Like efflorescence and improper waterproofing.

When we tore our the shower, we did have dampness. The red guard had failed. I didn't know about efflorescence but this makes sense why the issues are contained in the shower. Thank you.

So "filter" is not a generic thing - you are potentially trying to remove specific thing(s). And depending on what you are trying to remove, you use a different approach. Carbon filtering will remove chlorine, for example, but won't do anything for hard water.

The point is that you have to understand what you are trying to remove before you do anything else.

You say you don't want a whole house system or a water softener and you don't want something on the shower arm - so you have ruled out virtually everything but magic fairy dust before even identifying what you want to remove.

If you have a photo of the problem, please post it. You may also have an issue with either your cleaning products or your soap/shampoo etc. that is building up.

You probably want to dive deep into how to properly waterproof a shower.