datasette publish vercel til.db --app simon-tils
It can deploy databases directly to Cloud Run, Heroku, Fly and Vercel. It can cost pennies per month depending on database size and traffic.My https://til.simonwillison.net site (and many other sites I run) is deployed like that, using GitHub Actions: https://github.com/simonw/til/blob/81fdedb8e9b047cb059ef22c6...
See also the baked data pattern where I talk about this kind of deployment in a lot of detail: https://simonwillison.net/2021/Jul/28/baked-data/
For ad-hoc data analysis - assuming you already know your way around PostgreSQL - your pgAdmin in Docker solution is hard to beat.
How often do you create a new database?
My favourite thing about working with SQLite is that the overhead of new database creation is equivalent to the overhead of creating a file. In a given day I might casually create dozens of new databases, then throw away most of them. I never found myself doing that with MySQL or PostgreSQL.