If you have enough Apple devices to set up and configure Sign In With Apple, and you're interested in using the account with non-Apple devices, then using the Reset Password process to have a password assigned to your account generally has not — in my experience — impacted Sign In With Apple, which simply continues to work regardless. I have been able to use this process to sign in across Apple and Windows and etc without difficulty.
What's uncertain here is whether each third-party will correctly handle this workflow. I can't decide if it's worked every time because I'm lucky or because there's a regulation somewhere in the Sign In With Apple terms that requires it. I respect that this uncertainty may not be acceptable to everyone.
I can use Apple devices and still have the need to use non-apple devices so Apple's solution isn't helpful.