With saving, I usually add a confirmation directly next to the save button, so the save button itself doesn't change state (people often like pressing save multiple times!). But even then, I find a little bit of animation that moves the "saved" text away from the button to indicate where it's come from can be really helpful for intuitively connecting the two interactions. The animation should be fast (100-150ms max, often as low as 75ms), and subtle (just a slight step to the side), but it gives the user more of a feeling about what's happening.

> With saving, I usually add a confirmation directly next to the save button, so the save button itself doesn't change state (people often like pressing save multiple times!).

There is no problem with the button changing states as long as it only happens after the current document state was successfully saved and becomes active again when you make changes to the document. That way the button doesn't represent the outcome of some action but the sate of the document - unsaved changes = button enabled, no unsaved changes = button disabled.