[Q] How to refactor a Flask micro-service in Python

Hello, I would like to know your professional opinion on how to face a complete Refactoring of an app in Python, from how to implement the strategy to the end, please try to be very objective and detailed, I would love to know other experiences and techniques.
In my personal case I am refactoring a micro-service made with Flask, this micro-service is quite old. In addition to the fact that it has no documentation, nor a README.md, nor did they explain very well the context of why it was done… How would you approach this case? How would you implement an effective and good refactoring strategy? Only having the code itself as a backup?
What I did was analyze the code a lot and get as many outputs as possible. This micro-service also did not have a testing module to understand a little better what each functionality has to deliver. Switch everything to FastAPI for the ease and code shortening that this framework promotes. I was "translating" everything to FastAPI (but with the same functions, same methods, etc.). But now I want to improve everything, but everything is so tangled that it is difficult to see where to go.
Thanks for reading.