Returning to US from Munich

I do not think anyone can tell you what the risk of testing positive is.

But, if you test positive, you must self-isolate. I assume that you would need to find a hotel that would have room for you, and of course pay for the days. Here is a government website from Germany in English that describes the timeline for self-isolation after a positive test:

Persons who isolate at home due to COVID-19 can have their isolation
lifted at the earliest ten days after the on set of symptoms if they
have been asymptomatic for at least 48 hours.

Moreover, also persons who, while confirmed as carrying the virus, do
not show any symptoms (asymptomatic infection), can be released after
ten days at the earliest.

You would also need to check with the airline about what type of attestation or proof they require, and check about the rules for re-entering your country of residency after an infection.

thank you for the information