I propose to add set_ and get_ instead, but leave the storage in the public Rectangle.angle.

This is a consistency issue. We don't have attributes do fancy stuff (and thus have litte public attributes anyway). Defining set_ enables the use with standard mechanisms like rect.set(width=2, angle=30).

We don't need staling on .angle assignment. This has not been working and thus we don't need that for backward compatibility.

We may additionally deprecate .angle, but I'm undecided if that's worth it.

My approval still stands, although you made flake8 unhappy :)

Please add tests for the new setters and getters!

Test added. It's a simple figure comparison to make sure that setting the rotation after patch creation does the same thing as setting it in the constructor, with some additional tests for get_angle().