So, I noticed something when booting Puyo Puyo Tetris for the first time since I would close it to play another game, and go to the same menu when opening it again.

It seems that RNG in this game is seeded when you start a match (Much like older Puyo Games) and is also time-based.

Before beginning, set the music to what you want, and set the background to random. To get this set-up, you have to spam through the menus and pick two characters, puyo and tetris.

It seems to not matter which character you pick.

If you have yourself set up to have preset music and preset background, you'll get this instead:

This seems to be what happens on PC. I don't know about Switch or PS4, I have yet to try this on Switch. Will edit later.

This is known. You can see that I use RNG manipulation in my Extra Stages runs, and it's actually faster to close the game to manipulate a 1 cycle on 9-9. From what I know, the first game you play will be seeded based on how many times you've viewed the title screen and heard the voice line on the title screen (you can get infinite consistent seeds for your first game!), and every game after that is based on how long the game has been running. Again, this is only on PC to my knowledge. Also, going into the online menu ruins the manip.

I'll explain how to get infinite consistent seeds:
If you go through the title screen without hearing the voice line then play the game, you'll get seed 1. If you go through the title screen with the voice line, you'll get seed 2. If you go through with the voice line, then go back from the main menu, and skip the voice line this time, you'll get seed 3. If you go through with the voice line, go back, and listen to the voice line, you'll get seed 4. The basic formula is seed = voice lines heard + title screens watched.