Hi Robin and welcome to the Tiki community!
What you ask for makes total sense and there have been suggestions over the last years to have Tiki support this upgrade process, which is far more user friendly. But no developer has added that feature yet.
Therefore, the only ways to ugprade involve placing in your server the new version of Tiki (20.x in this case) in parallel to the old one (19.x in this case; avoid copying the new over the old one), and point the installer in 20.x to use the same db (or cloned db, in any case, after the usual backup of the db), and upgrade from there.
Documentation about upgrades is here:
If you can get a developer to code whatever is missing to have the other type of easy-upgrade you talk about, many users (and admins) will wave at you!