Do you see any "Errors" listed in the First Aid report or just the "Warnings"? Apple isn't clear on these things, but unfixed "Warnings" would imply no functional impact, while unfixed "Errors" will cause problems. I personally don't like seeing "Warnings" especially when it is not clear whether they are a potential problem.
Try running First Aid while booted into Recovery Mode. Make sure to run First Aid on the hidden Container. Within Disk Utility you may need to click "View" and select "Show All Devices" before the hidden Container appears on the left pane of Disk Utility. If First Aid cannot repair "Errors" from Recovery Mode, then you will need to erase the whole physical SSD (Intel only) before reinstalling macOS & restoring from a backup.
If you still get the unable to mount error afterwards when attempting to install macOS, then you will most likely need to perform a clean install as if you had unfixed "errors" instead of just "warnings" with the First Aid scan.
It is unfortunate Apple is so terrible with their error messages within macOS. Of the two errors reported by the installer/updater, I believe the mounting issue is the main cause of the failure as it is trying to prepare the "Update" volume.