For anyone else having this issue here is the root cause and fix. It would be helpful if Microsoft could confirm which months this bug existed.
Root Cause
This issue was identified and fixed last year. We realized we were incorrectly classifying SSAS models as AtScale. The bug was in production for 1-2 months before being fixed and any live connected reports created during that time were being classified as AtScale. Up until AtScale integration was finished ~1-2mo ago, we were treating AtScale virtually the same as SSAS with no parameters added to the connection string - so no change in report behavior. Some of these reports could have been holding onto the AtScaleDatabaseLive connection type for the last year, and now after republishing, they're unfortunately catching the new WSID connection string parameter. This lines up with the the inability to reproduce the issue today and why new reports are working as normal, but the customer republishing existing reports causes the WSID property to appear and failure in gateway.
Fix
Saving the file as a .pbip (PBI Project) file, exposing the metadata for the connection and change it there (something you can't do in the PBI Desktop UI.) Saving as a zip file, changing the Connection file there, and then resaving as PBIX just ends up as a corrupted file so that is not an available fix.