StatefulSets were added to handle things like this. It always seemed like an afterthought to me, appeasing people trying to run things that Kubernetes was never designed to handle.

At $BIG_CORP our executives became very excited about "The Cloud" and many teams were forced to migrate their applications over. Didn't matter if it was a proper 12 factor application or a monolithic vendor JAR that required 64GB of ram. You were punished for using VMs, so teams spent an inordinate amount of time shoving square pegs into round holes.

I used this one recently and it worked pretty well: https://github.com/zalando/postgres-operator

I did some research and most popular ones seem to be zolando and crunchy. I have zero experience, but going to deploy it for test environment to see how it goes.

https://www.kubegres.io/ has worked well for me. You can use custom images, provided they follow the conventions of the official postgres image. I haven't tried a major-version upgrade yet - my impression is that it will probably be a bit painful and involve some downtime and manual ops.

Some of the more advanced operators might better handle the upgrade problem? But in general, I've been happy with Kubegres for a ~10GB database with low traffic.