The first important question: What kind of hosting do you have? Shared hosting account? Managed WordPress? Private server?
If you’re using a shared hosting account or you’re with a managed WordPress provider (eg Kinsta, WPEngine etc), you can’t upgrade the database server yourself: it’s only your host that can do it. In that case, you may want to talk to your host about this or find a new host that runs a more recent server stack.
On the other hand, if you run your own SERVER (VPS, cloud server, or dedicated server), then you would be able to upgrade on your own.