That's a lot of things to upgrade!
I practiced on a virtual machine first, so I could gain some confidence in the process, migrate my customizations, and be sure not to lose any data.
There were some gotcha's on the skins side (they are documented in the upgrade guide) but the data come through without a hitch.
So I basically installed the newest weewx version on the new hardware, migrated the weewx.conf changes and custom skins, then restored the database, and it's all good.
You *might* get a problem between RHEL 7 and 9 because the hardware naming could change depending on your data source.