I'm not sure where the original poster is from, but where I'm at (Canada) my local library has a large gaming collection, including Switch 2 games. The bigger games you have to wait a while on the hold list, but there are plenty of games available at any time, for free.
I live in Santa Clara County in northern California, the county library has Playstation, XBox and Switch games for rent (you do have to take either a box or a slip of paper to the counter to get the physical game - they do not leave them out like movies.) There is a long wait period for the latest releases. I think I had to wait almost a year for The 100 Line: Last Defense Academy, and it took me two rental periods of 21+ days to play through it.