I don't have any relational database, but couch which also requires the things you are asking about - HA, clustering, backups etc. I am in process of launching my new app, so I have thought a lot about it as well. What I came up with is:

1) Database running inside docker, but using external mounted volume. Packet has external block storage(14$/month for 50GB high iops version), and you can configure backups on it ranging from 15m to every week. So that should completely cover the HA/backup stuff for most apps.

2) For monitoring/logging, the best solution so far seems to be datadog. It doesn't look very expensive, and seems to have most of the intergations you can come up with - couch, pgsql, docker, express, slack, github.

Combined it costs me 70$, which is a much better deal than PAaS I can think of,

Btw, if someone from datadog is reading this thread, your couch integration seems to be broken.