I think it happens on blank projects too (just tried, but it’s difficult to see as the delay appears to be affected by length of text).
New observations:
If you right click on the caret, the current word is not highlighted and the Context menu appears immediately.
If you right click in the word (but not the exact pixels of the caret) the Context menu appears after a delay and the word becomes highlighted.
Is this cursor/caret related?
Edit: Also tried in my current novel, and this caret behaviour is there too.