Remind me. When I create my API token, how do I provide it to git?
By copy-pasting it somewhere it has access to it. It can be the config file, it has several ways to use the system's secret storage, and you can also autotype it from your password manager every time if you want.
forced to save my token to persistent storage in a way I wouldn't be with a password
So not really
My point is, if you're going to store your password-equivalent in a password manager, how have you achieved greater security as compared with storing a password in the same password manager?
Passwords can be short and simple. API tokens are lengthy and random, and you can't change that. Also, you never type in your API key, and that can help against shoulder- and camera-surfing.
without doing anything to disable the existing point of access
You can't do that, because
- the API token is strictly for API access for outside programs
- the API token cannot be used to manage your account, like change password or emails, or to create additional tokens
API tokens are not a total replacement, just a more secure and restricted replacement for the everyday and not too risky tasks and for automated systems.