I'm the Global Administrator of our company's tenant and have been managing permissions for 18 months but have never seen a permission level called "Web-Only Limited Access". This suddenly appeared on one of our site collections, appended to all existing groups. It seems to be affecting functionality of OneDrive syncs and document library uploads.
It seems to have something to do with Access Control for Unmanaged Devices, which is configured to restrict end users’ actions (Download, Print, and Sync commands) in Office apps.
Do you have sensitivity labels set in your tenant, or see Confidential labels in this site? I haven’t been able to enable this permission level in my tenant, possibly due to subscription restrict, but found some articles describing “limited, web-only access”:
You may log in as an end user and see if you have lost download or related abilities in client application to help you confirm.