What changes for you? Nothing unless you start using threads. You probably weren't using threads anyway because there is little to no point in python to using them. Most python code bases completely ignore the threading module and instead use non blocking IO, async, or similar things. The GIL thing only kicks in if you actually use threads.
If you don't use threads, removing the GIL changes nothing. There's no code that will break. All those C libraries that aren't thread safe are still single threaded, etc. Only if you now start using threads do you need to pay attention.
There's some threaded python code of course that people may have written in python somewhat naively in the hope that it would make things faster that is constantly hitting the GIL and is effectively single threaded. That code now might run a little faster. And probably with more bugs because naive threaded code tends to have those.
But a simple solution to address your fears: simply don't use threads. You'll be fine.
Or learn how to use threads. Because now you finally can and it isn't that hard if you have the right abstractions. I'm sure those will follow in future releases. Structured concurrency is probably high on the agenda of some people in the community.
Im not worried about new code. Im worried about stuff written 15 years ago by a monkey who had no idea how threads work and just read something on stack overflow that said to use threading. This code will likely break when run post-GIL. I suspect there is actually quite a bit of it.
I feel some trepidation about threads, but at least for debugging purposes there's only one process to attach to.