Fresh install to latest version, but keeping everything else

I am Stück trying to update my home assistant, which is running on a BeeLink mini PC as Home Assistant OS, from version 12.4. to version 14, or any other version for that matter.
During installation the PC reboots suddenly and the update isn’t completed.

I was thinking that I could try a fresh install of home assistant and get everything to the latest version that way, but I would want to keep everything else. What kind of backup would I have to make of my current HA install to get everything back up and running on a clean install? I suppose a full backup would also restore the OS and Core versions, right?

Any help would be greatly appreciated!

I do not think the full backup include the HAOS and neither HA core, but even if it did then it would be the backup to choose.
The backup is just a tar file, which can be opened with most compression tools.
On Windows I use the open source program called 7-zip. https://www.7-zip.org/

When you open up the backup file you can extract the parts you want and manually restore just these.

Before going so far I would probably try to make a full backup. Download the backup and delete the one online.
If I had multiple backups online then do the download and delete the others too.
This is to make sure storage space is not the issue.
Then I would also stop all the addons you might have running. This is to increase the amount of memory available to the upgrade.
Then I would start the upgrade without a backup (you have the manual one already downloaded).