Update manager does not respect download mirror settings when upgrading to new Linux Mint release

Reproduce a Linux Mint release upgrade with a non-default mirror configured in Software Sources or Update Manager, then trace the release-upgrade path that chooses the download repository. Confirm the fix by verifying that the configured mirror is used instead of packages.linuxmint.com during the upgrade.

Describe the bug
When a mirror other than packages.linuxmint.com is selected in Software Sources (in the Software Sources app or in Update Manager itself), the update manager nevertheless attempts to download from packges.linuxmint.com when upgrading to a new Linux Mint release. This is problematic if packages.linuxmint.com is unreachable or performing poorly.

To Reproduce

1. Have a Linux Mint release upgrade waiting ("A new version of Linux Mint is available")
2. Have a source other than packages.linuxmint.com configured, or attempt to configure one.
3. Proceed with the upgrade.
4. The update manager downloads from packages.linuxmint.com instead of the configured repo.

Expected behavior
The update manager should download fron the configured repo.

Distribution:

• Linux Mint
• LMDE
• Other (please specify)

Software version:
5.9.8

Logs:

08.18@19:30 ++ Launching Update Manager
08.18@19:30 ++ Changes to the package cache detected, triggering refresh
08.18@19:30 ++ Starting refresh (local only)
08.18@19:30 ++ Initial refresh will happen in 0 day(s), 0 hour(s) and 10 minute(s)
08.18@19:30 ++ System is up to date
08.18@19:30 ++ Refresh finished
08.18@19:40 ++ Update Manager is in tray mode, performing initial refresh
08.18@19:40 ++ Starting refresh (retrieving lists of updates from remote servers)
08.18@19:42 ++ Refreshing available Cinnamon updates from the server
08.18@19:42 ++ Refreshing available Flatpak updates
08.18@19:42 ++ System is up to date
08.18@19:42 ++ Refresh finished
08.18@19:42 ++ Recurring refresh will happen in 0 day(s), 23 hour(s) and 59 minute(s)
08.19@10:21 ++ Changes to the package cache detected, triggering refresh
08.19@10:21 ++ Starting refresh (local only)
08.19@10:21 ++ Tracker: Mintupdate update button was pressed recently: 1 days ago
08.19@10:21 ++ Found 1 software updates
08.19@10:21 ++ Refresh finished
08.19@10:26 ++ Changes to the package cache detected, triggering refresh
08.19@10:26 ++ Starting refresh (local only)
08.19@10:26 ++ Found 1 software updates
08.19@10:26 ++ Refresh finished
08.19@10:29 ++ Changes to the package cache detected, triggering refresh
08.19@10:29 ++ Starting refresh (local only)
08.19@10:29 ++ Found 1 software updates
08.19@10:29 ++ Refresh finished
08.19@10:50 ++ Changes to the package cache detected, triggering refresh
08.19@10:50 ++ Starting refresh (local only)
08.19@10:50 ++ Found 2 software updates
08.19@10:50 ++ Refresh finished

Additional context
https://forums.linuxmint.com/viewtopic.php?t=339956