Yes, we unfortunately had a bug in the application download logic that wasn’t exposed until we introduced a second Incus LTS application with IncusOS 202605270119. Essentially there are now two “flavors” of the Incus application, and the code had been assuming there would ever only be one. This has been fixed by incus-osd/providers: Fix selection of proper application for download by gibmat · Pull Request #1120 · lxc/incus-os · GitHub , but existing systems will download both versions until they get an update with that fix.
IncusOS 202605270119 was briefly in the stable channel, and if your system updated to it you’ll see that error about more than one primary application being present. However, the system will still be accessible via API and should work as expected; the Incus versions are currently identical, so there’s no change in observed behavior. We’ve since demoted that IncusOS version back to testing so it’s not available for normal updates.
We fixed the duplicate application download issue and attempted to cleanup the accidental LTS application in IncusOS 202605272150 (currently only in the testing channel), but I had a major facepalm because it removed the Incus LTS application from 202605270119, but not the freshly updated 202605272150. 
This exposed another bug that’s expressing itself as the lstat error upon reboot.
Last night I made the accidental Incus LTS application cleanup more robust ( incus-osd: Make the cleanup logic for accidental incus LTS more robust by gibmat · Pull Request #1125 · lxc/incus-os · GitHub ) and am working on a fix for the secondary bug causing the lstat error. Hopefully there will be another IncusOS release to the testing channel fairly soon that should cleanly update and get things back into a good state.
Getting IncusOS back to a good state
If you’re currently on the stable update channel and had updated to 202605270119, ignore the error about more than one primary application being installed. IncusOS will still operate correctly, and the next stable update will properly clean things up.
For IncusOS systems on the testing channel that boot with the lstat error, some manual recovery work will be needed. You’ll need to follow the steps at Emergency Procedure for a Lost Client Certificate - IncusOS documentation to use an encryption recovery key to manually mount the IncusOS system drive. Once mounted, remove any incus-lts-7.0.raw image(s) that exist under /var/lib/incus-os-extensions/ (find /var/lib/ -xdev | grep lts), then reboot and IncusOS should come up cleanly. Because this error occurs very early in the startup process, I don’t think we’ll be able to push an automatic fix for this problem.
Edit: A few people have also reported that booting back into the prior stable release, 202605181246, allows IncusOS to startup and resume operations. When a new stable release is published, those systems should automatically apply it upon next reboot.