I'm just going by the term "Bürger" which in my lousy German is "citizen". As a citizen or a resident, I am neither (I am assuming "resident" here means the same as it does in US immigration) - as I am on business travel for a month or so. I fully believe you are right, as the limited information I have read says that testing is free for anyone. Bavarian information says citizens/residents get free tests upon demand whenever they want. The Health Authority for my area (80805) did not give any real options. Additionally, I do not want to be tested by possibly misrepresenting myself.

Since getting tested is required to both break quarantine and visit my worksite, getting a timely test is critical - so the paid route was preferred by my employer and the worksite, as neither were able to confirm I could get tested in any other way. Since I am permitted to break quarantine after 5 days solely to be tested, I don't want to be running around the city looking for options.
As for the paid route, it was shockingly easy and results were delivered in 6 hours.

I'm just posting my experience in the hope it is useful to others. Isn't free testing ending on Dec 1st anyway (for everyone or travelers only?) or did they extend it?