I was finally able to fix the game.
As it should be working on NeutOS and its included patches, I kept trying on it, even though the game wasn't even starting when I tried on it before.
- First I uninstalled the game and removed every ticket and savefiles.
- After that, I entered Maintenance Mode (with AutoRCM enabled - I held both vol buttons as soon as I injected NeutOS payload untill MM booted) and left just turning power off, without doing anthing there. After that I injected the payload again and booted NeutOS.
- Then, with tinfoil, I installed game and update only, and the game started working on NeutOS (which means some traces were left corrupted in the system even after uninstalling and removing tickets)! Installing all the wave 4 dlcs after that lead to another error when booting the game (2002-4144), so I uninstalled everything and followed the steps above once again untill installing game and update.
- After that, I installed each dlc separetedly considering their version order with "reinstall NCAs" option turned on, testing the game after each installment, but I didn't install [Additional Story Content +], as it was conflicting with [Side Story Cindered Shadows]. Both came with Wave 4 when I downloaded, but it seems that Cindered Shadows has the first inside it too...
- After that, everything is working normally once again! After almost 2 weeks of hundreds of attempts, I can finally play my old savefile with everything unlocked!
I didn't mean that this thread would have so much about this (sorry!), but I hope my findings can help someone who search for "Checking whether the software can be played" and "Unplayable downloadable content was found" in the future. Thank you guys once again!