How can I retrieve a user ID from Firestore via Flask backend (React frontend)?

Question

I'm a newbie with authentication! I'm building a web app where users can log in, and the data shown in the web app is different for each user. I'm using Reactjs as my frontend with Firebase authentication. After a user logs into my web app, I'm storing their user ID (UID) and other information into Firestore. I have a collection usersCollection where each document is labelled with the UID. For the backend, I'm using Flask as mostly a REST API with a Postgres database, but I am not storing user credentials there (UID, password, etc.).

For some of my backend functions I need to change the output based on which user is signed in, but I'm not sure how to retrieve the current user's UID. I'm able to make an axios request to send the current user's UID from the frontend to the backend, so I've tried 2 methods with that:

1. Saving the axios request output as a global variable - this has led to Flask errors like runtimeerror: working outside of application context. and I don't think this is the best solution.
2. With each GET request that the frontend is making to the backend (every time there's a function whose output changes based on user), I am passing the UID as a parameter, which causes latency problems.

What is the simplest way for me to request the current UID from Firestore from the backend?

Is structuring our frontend, backend, database, and authentication like this recommended? Or is there a simpler way or better system for our situation (JWT?)? We selected Firebase authentication in the first place because we are using a React MUI template that already set up Firebase for us.

Thank you in advance! Happy to provide more information if needed!