FCPx app is up-to-date, but cannot open libraries from a "more updated" version?

Hi all,

Hoping someone can help me out with this one...!!

I've been trying to open my Final Cut libraries all day but still cannot seem to get access — this is the message that keeps coming up:

The document “____” could not be opened. One or more of the libraries were created with a newer version of Final Cut Pro. These libraries will be ignored.

I updated the iMac with the latest software update (macOS Big Sur 11.4), and I've gone into the App Store to see that the FCPx app itself doesn't need any more updates...

Any ideas on what I'm missing?

I normally work on a different iMac at work, but I've been lended this other one from the office (thanks, Covid).

This is never happened before and I'm not sure what to do about it (eek)!

Any help/suggestions/advice/feedback is much appreciated!

TIA!