Does changing focus affect a lens’s focal length?

In general: possibly yes.

You actually adjust focus of your lens, not your camera. It can be an advantage1 to design a lens in a way that it changes its focal length slightly when focusing. This is not very important if you take still images. This is different for video of course and one reason why cinema lenses are so expensive

But even if your lens is not guaranteed to have a constant focal length, it might still have it. Maybe it's just having that issue at certain focal distances and you'll be able to happily modify focus at other distances without seeing any change in focal length. To what extent a feature is partially existent on a product is something you will never see advertised or in a spec list. If a constant focal length is important to you, you should rent the lens and try it out if it is not explicitly labelled to have this feature.

1 advantage as in the lens designers do not have to worry about it. It costs money to make lens designers think about things. If a company decides that a feature of a lens is not important and the lens designers do not have to think about it, it can make the lens cheaper, which can be an advantage (if you don't care about the feature either)