Bought songs on Google Play Music years ago, can I still get them?

Depends whether you moved your library over before Play Music shut down in 2020. Google offered a transfer to YouTube Music back then, and purchased and uploaded songs came across with it. If you did that, open YouTube Music, go to Library and switch the view to Uploads, they should be sitting there and you can download them. If you never transferred, I'm afraid the Play Music data was deleted a while after the shutdown. Worth a quick look in Google Takeout to see if anything is listed for your account, but I wouldn't get your hopes up.