It actually does, because the use has to satisfy the specific terms of the trademark, which might not be accomplished by just a logo on a random web page. And it has to stay there even in the face of internal pressure to “turn the page” on the old brand, or the general drift of focus/priorities over time.

This is one those things that is simple in concept, but can be deeply complicated by internal factors. I’ve got years of experience doing this.

Trademarks are like a ratchet; if you let them slip too far, it can be extremely difficult to turn them back. And things tend to slip if left unattended.

Edit to add: note that I also said “a will to do so.” It’s not even clear whether Musk will want to defend the Twitter trademark. Certainly doesn’t look like it so far.