I’m not sure, if the basics are clear, so I’ll just make it clear for everyone.
To upgrade manually, by re-installing the OS, but keeping the /home partition, all you have to do is do everything as usual, so at the partitioning section you choose “Something else”, make absolutely sure, that the /home partition is neither formatted, nor otherwise modified or created and then you let the installer mount that /home partition in the installation process, instead of creating it from scratch. That’s it.
Needless to say, a backup should be created beforehand, in any scenario.
The annoyance starts, when you need to re-install the software you need.
As can be seen here, it’s usually not easy to manually deduce, which packages were actually manually installed by the human using the Linux operating system.
However, that’s the next step, anyway.
I would suggest starting out installing and mounting /home as explained above and see if it works. If it works, you may continue with further modifications.
The only rule is to always take backups, before doing anythihng. Having too many backups is not a problem. Having a single one missing is a big problem.