My best guess for what is going wrong is that you have too aggressive Plex scans enabled on auto.
Plex was designed to access local disks or network storage, not a mounted cloud-drive, so some of it's scanning types can be very agressive - reading loads of data and querying files very often to gather things like metadata, previews ect. While this is not such a big deal on local storage it can certainly be a problem on a cloud-based system since you obviously have much less transfer speed to it + also API restrictions (1000 requests pr 100 seconds). If Plex decides it wants to read all of your files 100% to generate previews in an advanced scan that could literally result in your entire archive being read via the internet - which would probably not be what you want.
The solution is usually that you disable the most agressive scanning options that can not do it's just jus based on the file-attributes from the listing it gets (and thus needs to actually access each file in sequence). Such scans should only be performed manually, and sparingly - in a "downtime" period when nothing else is going on.
If you can find the spesific error type (you will want to look/search for 403 in the log) I can say a little more about the spesific error. There are several type of 403 errors however. Be sure to paste the full error line including the text-description.