Pretty similar to N64 games (Mario, OoT, MM) or gamecube games (Mario Sunshine). Speedrunners have modded consoles or hacked ROMs for tricks/glitch execution practice.

This is really helpful for practice. I would love to know if it is possible to do this on PS1/PS2 consoles and if it already has been done on those consoles, which games have practice cheats.

Also asked on reddit: https://www.reddit.com/r/speedrun/comments/7lsvvg/are_there_any_ps1ps2_speedruns_that_use_cheats/

as far as I know it is possible to play bootleg/selfmade/homebrew games/programs on PS1 with a modchip that disables the check for an original game disc. This could of course be used for that purpose, if someone makes a modified iso for the game in question. Note that this still does fall under piracy, if someone uploads or send a modified copy of the game. I don't know anything about cheat devices (like Action Replay for NDS), but those might also exist and could help with that.