The remaining solution was Magisk. Magisk was equally easy to install, but recently deprecated that easy install method so that only patching the ROM file remains (you get that file from the ROM you run, unpack the archive, if you are unlucky you need to unpack a second payload.bin file, https://wiki.lineageos.org/extracting_blobs_from_zips#extrac...). But not only is that more complicated, it also does not persist after a Lineage upgrade, which happens every week, see https://github.com/topjohnwu/Magisk/issues/3820#issuecomment.... Totally crazy for a project not in early alpha.
I want root to properly manage my battery via https://github.com/VR-25/acc ( with ideally https://github.com/MatteCarra/AccA as Magisk module). How ridiculously complicated that is now and that the install procedure is broken without them documenting it soured me quite a bit on Magisk, but I also start to develop some bad feelings about Lineage - because it is them that would be in the best position to provide a simple root solution. But they just refuse it, and even forbid discussing such topics on their subreddit - that alone shows me that the project is very user hostile currently. I doubt with that attitude they can make a turnaround, but I'd be happy to be wrong...
Sadly the other bigger ROMs are to my knowledge not better in this category, neither /e/ with their service suite, nor DivestOS with the passionate developer nor CalyxOS or GrapheneOS with their "security" focus are interested in giving the user full access to their device. Android seems to be a dead end here, real Linux is needed.