Exactly this worked best for me back in the day

Not just you, your brain is wired to pick up language, how did you learn your first one?

I’m German and while we have some mandatory English classes, they’re …well … not good.

I can attest that English classes here aren't great either (although most people here do speak English as a second or third language)

and at least the teacher I had first also had a VERY thick German accent

This is a known side effect of premature output (writing/speaking before you feel comfortable doing so), you don't just listen to what's around you, you primarily listen to yourself and pronunciation differs between languages, this premature output becomes toxic input for your brain which then uses that from then on (you can try and get rid of it; but it is really hard to do)

once I was halfway through the game my brain kinda switched to “English mode” and I actually learned words and grammar in a natural way instead of trying to force myself to understand what the hell a “singular past tense adverb” is.

Yup, that's natural understanding for you. When you speak a language you don't care about the rules; you should instinctively know them.

As for my issue with Duolingo: it ignores the amount of time it takes to properly acquire a language, if I were to split up all the time I spent watching english youtube into 5 minute chunks it'd take me well over 15 years (and that's just accounting for the initial 4 month span; I've learned more things after as I naturally used the language). Combine that with the fact it throws established research on this topic to the wayside to push the school-based one which we know goes against the natural way in which we learn. I found a great blog post online about this, while it mostly revolves around learning Japanese; the core principles apply to learning pretty much any language. The beginning of the post does sum the entire thing up pretty well though:

We do not recommend "language learning" apps like Duolingo, Lingodeer, Babbel, and others due to the fact that their methodology conflicts with AJATT's principles of immersion learning. Such apps do not actually help you with anything. There are no success stories. On the other hand, AJATTers typically reach fluency in just 18 months. The apps prevent you from reading interesting content in your target language, such as manga. And they make you more miserable in the end.

There are some really good parts in that blog that apply to any language; but a lot of it is geared towards Japanese specifically.