Lightweight SQL server to serve .sql content
I use DB Browser for SQLite. It's free and has the feature I need, but it's pretty lightweight, so you won't have some features like SQL Procs, etc. I think it supports triggers though, so I guess you can get around the no-sql-proc issue by writing some triggers.

The database runs on SQLite, which is a pretty popular free version of SQL, so you should be able to find compatible Python packages for it. Like these for example: 11.13. sqlite3 or 12.6. sqlite3, but I don't use Python so I haven't tried either of them.

Anyhow, it works well for me. I use it for managing data that's too messy to parse with excel. For doing analysis I use the Julia programing language (but Python should work just as well).

Edit:
If you do decide to try SQLite and are wondering how to get your MySQL data into SQLite, here is a StackOverflow page that talks about exactly this.