How long are you keeping your old LR backup files?

I use a utility called 'Hazel', that can perform all kinds of automatic actions on folders. What it does in my case is keep the number of catalog backups down to a certain number, by automatically deleting the oldest copy if that number has been reached and a new backup is added. I do make catalog backups (but also general backups of my entire disk) because Lightroom does not only make a catalog backup, but also verifies the integrity and optimizes the catalog.

LR backup folders containing WHAT? What is in those backup folders? Inquiring minds want to know (and can't answer your question unless you tell us that information)

Essentially, with regards to any backups of anything (not just Lightroom Classic) ... you keep as many as you feel comfortable with, after all, the risk is yours.

I don't use the LR backup schema at all, it only backs up the catalog and a good backup should do far more than that. You want to backup everything you can never afford to lose. Images, catalog, presets etc.

But to answer your question, you don't need old catalog backups. You want one at least, maybe two IF you continue down this road using LR to only backup a catalog. Save space, trash the older ones.