Hey, thanks for the report. This is known behavior and not a critical bug. On Linux, if you install via apt, the in-app update check uses a separate feed that can publish a new version before the package shows up in the apt repo. Because of that, for a few hours after a release Cursor may show a “new version” even though apt is already on the latest. The popup also shows on every start because the deb build doesn’t self-update. Self-update is only available for the AppImage.
To update, use apt as usual:
sudo apt update && sudo apt upgrade cursor
To stop the popup, set Update: Mode to none in settings. Settings > search “update mode”. Downside: this disables all update notifications, including real ones.