Chances are you will have to ebay or emulate for a bunch of games. Now of course I wouldn’t just leave you with those options. There is a 3rd option since you have original hardware. You can mod. There are a couple of those options open to you as well.
What a lot of people are doing now so they don’t damage physical discs is replacing the hard drive with a modded one which you can play games from. So the games would be preloaded and you would just select the one you wanted to play and it would play it from the hard drive.
The other thing you can do is jail break your PS2
How To Burn PS2 Games & Play Them! (No Modchip) - YouTube(The second half of the video)
Then you can take games you download, burn them to a disc and play them on your PS2. You would have the luxury of physical media but it’s not the original disc.
The last option which imo is the worst option in 2022 is a modchip. You can fuck up your PS2. Not a good choice considering the first four options.
Of course you can just go to ebay and buy the fucking game for under $10. But I like complicated solutions.