> The response.getheader method in urllib has been deprecated since 2023 … When the method was eventually removed, lots of code broke.

Two years doesn't seem long to me for a widely used project, unless you have an LTS version that people needing more stability can use, or you are upfront that your API support is two years or less. Of course API support of less than two years is fine, especially for a project that people aren't paying for, but personally I would be quite explicit from the outset (in fact I am with some bits I have out there: “this is a personal project and may change or vanish on a whim, use it in any workflow you depend on being stable at your own risk”). Or am I expecting a bit much there?

If using semver or similar you are fine to break the API at a major release point, that is what a major release means, though it would be preferable for you to not immediately stop all support for the previous major version.

> What if we intentionally made deprecated functions return the wrong result … sometimes?

Hell no. A complete break is far preferable. Making your entire API essentially a collection of undefined (or vaguely undefined) behaviours is basically evil. You effectively render all other projects that have yours as a dependency, also just collections of vaguely defined behaviours. If your API isn't set in stone, say so then people have nothing to complain about unless they specifically ask you to keep something stable (and by “ask you to keep something stable” I mean “offer to pay for your support in that matter”).

> Users that are very sensitive to the correctness of the results…

That is: any user with any sense.

> might want to swap the wrong result for an artificial delay instead.

That is definitely more palatable. A very short delay to start with, getting longer until final deprecation. How short/long is going to be very dependent on use case and might be very difficult to judge: the shortest needs to be long enough to be noticeable to someone paying attention and testing between updating dependencies and releasing, but short enough that it doesn't completely break anything if someone updates and releases quickly, perhaps to bring in a bugfix that has begun to affect their project.

This is still evil, IMO, but a much lesser evil. I'd still prefer the complete break, but then again I'm the sort of person who would pay attention to deprecation notices, so unless you are a hidden nested dependency I'd not be affected.