There is https://openf1.org which has an API, although I don't believe it's real-time. My projects uses the SignalR stream directly from F1, but it's not very API friendly and you have to learn and do a decent amount of processing to make it in to useful display data. Check out the UndercutF1.Data project to see how this is done. FastF1 also has a live timing client, although I don't think its their preferred method of analysis.

After a session is finished, F1 do upload json and jsonStream static files which you can download - checkout the DataImporter class to see how this is done (this is what powers the undercutf1 import` command)

Check out FastF1 - https://docs.fastf1.dev/

It has a Live Timing Client and a lot of historical data.

I only found it the other day, so I have no had a chance to play with it yet.

It's not meant for public use, but it's also not protected. Best documentation is the fastf1 project.

certainly not free, but with F1TV Access you have access to historical and real time data through the API. There should be decent documentation on it out there, otherwise projects like Multiviewer or this TUI wouldn't be quite realistic.