>I'll probably just have to bite the bullet and form an LLC with a rented address and phone number once I get ready to release a paid app, which unfortunately just increases my costs even more for what is most likely to remain just a small side hustle.
This is actually still not a valid solution. You'll have to provide an address where you can be physically reached, even if you publish your app as an LLC (at least under German law). A "rented" address won't fulfill that criteria. If you run your LLC out of your personal home, you'll need to publish your personal address (again, under German law, it may be different in other EU countries).
This does make sense in principle, as it allows your customers to actually track you down in case they feel the need to sue you.
You might get away with listing the address of a co-working space, if you are actually physically present at that address during normal business hours.
You might also get away with listing your legal name and the address of your lawyer. But your lawyer would need to agree with this and you'd have to have an arrangement in place that they will represent you in any and all future cases, which might be difficult. This doesn't seem to be a settled question in german jurisprudence.
Also, you could just chance it. Not listing an address will simply result in potential exposure to a cease and desist letter, which (under German law) only results in limited financial liability. I am not a lawyer, so please get a professional to check, but if you are really serious about not exposing your personal address, it might be simpler and cheaper to run the low risk of a cease and desist instead of making a big fuss about an alternative address.