The trial version is the same product as the non-trial version, the trial license is the only difference.
If you bought Pro there is NO need to uninstall your trial.
I think if you buy ARTIST and your demo was pro, you should probably uninstall as there is a separate Cubase 11 ARTIST installer in the Steinberg Download assistant.
So, Pro Trial to Pro retail : No reinstall.
There is no need to switch to the other usb eLicenser, you can sell the extra unused elicenser.
I see no benefit in owning the second elicenser unless you want a spare that you can activate (with steinberg’s help) if the first one became lost or damaged.
If you buy an ARTIST license, the only difference will be that you might have some content that comes with PRO only and not with artist, and you can fix that by simply removing the unlicensed content when the time comes to do that, you don’t need to reinstall the whole cubase app.
If you had a demo/trial of Cubase ELEMENTS then yes you would need to uninstall and get the PRO/ARTIST installer.