The real selling point for managed database solutions is that they take care of backups and the like for you. Local databases are still perfectly sufficient for non-prod environments, and if you need specialized tuning or use foreign data wrappers extensively managed isn't an option. But if you just need A Database Somewhere the cloud is usually as good a place to put it as any. Money spent there is money/time you're not spending on routine care and feeding.
The only vendor I've worked with is Amazon. I can't give them an unqualified recommendation; the AWS interface is obtuse and their modifications to the Postgres core sometimes cause problems.
I was actually going the route of having a DO droplet where I have my node app and its postgres db all in. And that would be already my production environment.
So as long as I am willing to invest "routine care and feeding", it should be ok?
I don't know anything about DigitalOcean specifically, but in principle yes. If it's a container or vm, make sure your data directory is in a permanent volume instead of ephemeral storage.
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