I have an HDD with bad sectors, but most files are still readable.
Can those files be corrupted, even if there are no read errors?
Depends - how many bad sectors do you have?
I have a HDD with 16 bad sectors. Its had them for 3 years and is still running like a champ
I didn’t do a chkdsk. I just looked in the event log, and there are “disk has a bad block” errors.
get crystal disk info standard edition https://crystalmark.info/en/software/crystaldiskinfo/
then look for pending sectors and uncorrectable sectors. if you have any uncorrectable thats bad but not the end of the world. if it has any pending sectors especially if the value is higher than one. then get everything backed up from that drive asap.