It depends on the business use case and requirements.
Using a managed database solves this problem, so there's that an option.
If you self host your DB, if the data is on block storage you can at least spin up a new instance and connect that storage device onto the new instance with a short period of downtime. This is usually a satisfactory level of downtime for an event that doesn't happen too frequently.
What I like about the above is it'll work with any database and avoids needing to even think about performing real-time or near real-time replication with multiple writers.
There's also the scary truth that there's a ton of stuff out there where compliance requirements aren't enforced. I'm not saying it's a good idea but you can choose not to upgrade too. This is a risk assessment you'd need to do. At the very least if you go down this route, please make sure your server doesn't even have a public IP address. If it's super locked down, that doesn't mean it's safe but you'll want to limit the number of attack vectors as much as you can.
How would you upgrade the server running the database?