Dev/QA/Similar: Either containerize and back to persistent volume, or use a managed DB service such as RDS or Cloud SQL and create a schema per environment. Include a deployment pipeline argument to reset to known state. CI pipeline can be tuned to handling dynamic environments in either case.
Stage/Prod: Use managed DB service such as RDS or Cloud SQL.
The time and cost to automate a DB upgrade with every edge case considered is huge. Rarely makes sense for small/medium business.
Nitpick: I really don't suggest a divergence in the DB/stack-of-choice between Dev/QA/Stage/Prod. I've chased so many issues that were in the planning process dismissed as "yeah that's an edge case and most likely won't happen".
The reasons I've seen for doing so are usually penny-wise, pound-foolish. Penny-wise in saving a few dollars (conceptually) on a spreadsheet for per-env/per-cycle, while neglecting the long-tail consequence of your labor factor just growing, potentially forever, without regard for total cost of ownership.
