Asklemmy

I know it's probably not what you're asking for but there's an album where a bunch of Japanese anime voice actresses did covers for popular songs from the 80s and 90s. It called Voice Actresses Legendary Punk Songs Collection and here's a playlist that has most of the songs (one of them is unavailable for some reason).

Outside of that, I mostly only know bands who have covers of video game music (and some movies) from the 80s and 90s. If you are counting those, here are some examples of them:

Lighting Strikes Again and Metal Squad from Thunder Force IV by SSH. SSH is known for metal covers of old video game music, so this is just one example of his music.

Cranial Syphon by Armcannon, which is a cover of some song from Metroid but I'm not familiar with that game so I don't know what it is exactly. On top of covers for other video game music, they also have stuff like the Ghostbuster's theme.

Kraid by Metroid Metal, which is obviously another metroid song (possibly the same one). There music was a bit hard to find on YouTube, I've forgotten where I first heard their music before but Youtube might not be the best platform to find the rest of their music.

Battle Scene from Final fantasy by The Black Mages. While they are currently disbanded, they were known for rock/metal covers of music from the Final Fantasy games (which makes sense given that the band was created by Nobuo Uematsu himself). They did briefly rebrand as "Earthbound Papas" for one album because not only did they want to cover more than just the Final Fantasy games but they also wanted to branch out to more genres.

I know for sure that there are some that I'm forgetting and there's also some that I don't feel like looking for examples for (mainly artists who've covered the music from the 90s era Touhou games). If asked, I may do through and provide them but I think I've provided more than enough already.