Most likely, your PS1 game has disc rot or deeper scratches not even the system can look past anymore, and the console is fine. You can sometimes resurface these games, but it depends on the condition of the scratch. Just to sanity check the PS2, if the unit works fine with other PS1 games (and PS2 as well), put a super bright light on the disc and look for deep holes in the media. Modern LED lights expose these issues very easily, especially the 1,200+ lumen ones. Something like this:
If you see a bunch of pinholes, the game has "disc rot" and it will never work correctly. If you do not see any, it’s likely due to the media being scratched. Providing it isn’t disc rot, you MAY be able to have it resurfaced - take it to a record shop and ask how much it costs and let them know you are okay with the risk it may not help. For example, my local record shop only charges ~$3/disc, give or take (it’s been a while since the pandemic, but it’s so cheap I would take the chance on a disc worth far more than the cost, especially if I’m buying something anyway). It may very well be worth lighting a few bucks on fire if it’s a game that’s expensive or a little hard to find. The only difference between a PS1 game and an audio CD is the black dye, and most know this and while they may not SELL games, they often resurface them when you bring them in knowing this if you bring it in.