Despite the downsides of F-Droid, there's one thing they provide that other stores like Accrescent simply can't. F-Droid provides APK builds with the exact source used for the build available. There's a lot of trust involved, but this trust is in a single entity, rather than random developers. F-Droid has existed for a long time without adding malicious code to builds, so when they say "this source code produces this APK", they have years of history doing exactly that to back their claim.
A random app developer has no such trust built up. Stores like Accrescent, even if you download only FOSS apps, trust the app developer with building apps. It's less prone to one massive takeover, but APKs built by random devs are much harder to verify and check for malicious code than the source code. If F-Droid is taken over, it should be noticed relatively quickly, but affects everyone using F-Droid. If an app on Accrescent bundles malware, only users of that app are affected, but it may go unnoticed for a much longer time.
Research on this topic exists, and it is possible to alter the output of an LLM in minor ways, that statistically "watermark" the results without drastically changing the quality of the output. OpenAI has probably implemented this into ChatGPT.
https://www.youtube.com/watch?v=2Kx9jbSMZqA
I think the tool exists, and is (at least close to) as good as they claim it is. They can't release it, because once the public can tell with high accuracy whether ChatGPT wrote some text, another AI can be developed to circumvent detection from this method, making the tool useless.