You're right, the tap water isn't completely sterile and still has some contaminants but it's nothing to be super concerned about if you're not regularly shitting yourself after drinking tap water everything is fine

You definitely want some contamination in the form of minerals as they give your water its taste. You can buy a fairly cheap "TDS" meter online which will show you the Total Dissolved Solids. This won't give you a complete picture of what's there but will let you know if your water is more or less "minerally " ( I.e soft or hard )

Outside of that you can look into getting an ICP test which will give you a break down of the exact minerals in your water, depending on the brand they may also test for bacteria but most don't. The ICP still won't pick up on other contamination like PFAS but they're incredibly difficult to remove anyway so it's best not to think about them...

You can also look into installing an RO-DI system which will filter out minerals and other organic compounds like ammonia etc but it won't do anything for bacteria or PFAS. You shouldn't regularly drink de-ionised water though as it strips the minerals out of your body ( like the calcium from your bones ) so you'd have to re-mineralise it.

Your water is totally fine and safe, don't overthink it!