I would seem to have resolved this issue after getting a clue of what to do from some recent posts here and thought I'd indicate what was happening and how I fixed it to the forum in general - just in case somebody else is having the same problem.
In short, whenever an CPT archive was clicked to be opened, I would receive a critical error from WP. Fortunately, it didn't crash the site, just throw the error. I couldn't even view a custom post from the dashboard. My CPTs were made through Elementor and are relatively simple in construct.
My VPS hosting is on Contabo and I use SpinupWP. The setup for this site was the typical for me these days, with PHP v8.0 - and that seemingly proved to be the root of the problem. When I downgraded PHP to 7.4, the problem disappeared.
FYI, I'm running 5.6.14 of MB and 1.16.8 of MB AIO.