Okay, I figured out how to make subtitles for a fanedit. At first I tried Whispher AI (same guys as Chat-GPT) and while the captions were very accurate, the timings were not (text stayed too long on screen).
So next I used Adobe Premiere Pro. This worked surprisingly well. I think any piracy links are not allowed, so I'll just say that I installed Adobe Premiere Pro 2023 (v23.4) Multilingual and then Adobe Speech to Text v12.0 for Premiere Pro 2023. This worked for me but there are different versions of Premiere Pro and Speech To Text so they might not work sometimes. Next, I followed the tutorial (YT: New Captions in Premiere Pro 2021 - Auto Transcribe Your Videos) and generating subtitles was really simple and fast. Premiere Pro gives you SRT file with timings.
Now there may be a problem because Premiere Pro doesn't read MKV files, just MP4 and some fanedits use MKV. To fix this you have to install ffmpeg and then use command "ffmpeg -i input.mkv -c copy output.mp4" to very quickly turn MKV into MP4 without quality loss. Then you can generate the subtitles using Premiere Pro and MP4 file.