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I found an academic article (Vogel et al 2019) that analyses this phrase. Key points:
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when the German legislator uses geschäftsmäßig, this demonstrates a clear difference in intention from gewerbsmäßig or gewohnheitsmäßig
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the article quotes Franz von Liszt 1881, and this definition seems to be accepted to this day:
Die Gewerbsmäßigkeit charakteriſiert ſich einerſeits durch die auf öftere Wiederholung gerichtete Abſicht, andrerſeits durch die Abſicht des Thäters, ſich durch dieſe Wiederholung eine, wenn auch nicht regelmäßig oder dauernd fließende Einnahmsquelle zu verſchaffen […].
Die Geſchäftsmäßigkeit teilt mit der Gewerbsmäßigkeit die auf regelmäßige Wiederholung gerichtete Abſicht, dagegen fehlt die Abſicht, ſich eine ſtändige Einnahmsquelle zu eröffnen. Ob die einzelnen Handlungen honoriert werden oder nicht, iſt gleichgültig.
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the term geschäftsmäßig is significant for §5 TMG, but has also reached wider attention in the discussion around the decriminalization of assisted suicide.
So the key defining aspect is the auf regelmäßige Wiederholung gerichtete Absicht, the intention directed towards regular repetition.
This meaning in legalese German is divorced from everyday language.
§ 5 TMG has the interesting construction of “geschäftsmäßige, in der Regel gegen Entgelt angebotene Telemedien”. So the TMG does not seem to care whether you have a profit motive, only that other people might provide this kind of service for a profit motive. If other people would provide instances of Discord bots in order to get donations, that might already bring you in scope.
This is not legal advice, but it seems like your options are to either avoid running an instance of the bot, only running it in a private context without access from a wider public, or sucking it up and providing the necessary documentation.
And no, it is probably not possible to use a PO box because you don’t live or work at that address. The general expectation seems to be for the address in an imprint to be ladungsfähig, so that you can be served there. This random lawyer’s website writes:
Unter der Anschrift in diesem Zusammenhang ist die Postleitzahl, der Ort, die Straße und die Hausnummer zu verstehen, nicht ausreichend ist die Angabe eines Postfachs.
There is no downside to nested encryption, except of course the performance overhead. But this only really makes sense if each layer has an independent key and each layer uses an algorithm from a different family. Improper key reuse weakens the scheme.
For symmetric cryptography like AES the benefit is dubious. It is far more likely that the content is decrypted because the key was acquired independently than that AES would be broken.
However, there absolutely is a benefit for asymmetric crypto and key agreement schemes. This is how current Post-Quantum Cryptography schemes work, because:
Nesting one algorithm from each family gives us the best of both worlds, at a performance overhead: conventional asymmetric cryptography give us temporary security in the near future, and the second PQC layer gives us a chance at long-term security.