Hi Kevin,
Thanks for looking into this. I got a bit distracted (no small irony that I just cobbled together a 100+ page report in Word), but hopefully this is still considered active and I won't need to post from scratch.
I went to options>add-ins>COMs and disabled everything. I restarted, and then restarted again in Safe Mode (holding down control while Word loaded). Hopefully this address the add-ins/third party software question.
There are two possibly related issues that accidentally got joined in your reply. There is comment-like shading, and there is a spelling pop-up window. I took screenshots of all three states:
Here is the basic screen. The familiar squiggly underline is as it should be. The screenshot didn't capture the i-bar, but it's blinking merrily just above the text. You can see from the title bar, Word is in Safe Mode.

I added a comment for comparison (the comment bubble is off to the side, but it's the one on the right with the red line pointing to it). My mouse is now hovering (no clicking, just hovering) over the misspelled 'lazie', and you can see its background colour has changed.

Lastly, I left clicked on the misspelled word, and this shows the pop-up that has been appearing:

The colour and the pop-up are extremely distracting, but I can't find out how they started appearing or how to turn them off. I work extensively in word and the innocuous underline squiggle is sufficient to let me know when there's an issue. Most of my work involves foreign countries with non-dictionary person and place names, so there is a fair amount of underlining. As I review and merge peer-review comments and corrections, my mouse is frequently moving over text. The flashing highlight and pop-ups are very distracting, and I really hope you'll be able to help me suppress them!
Oh, this is a recent computer build and fresh installation. I have run both quick and online Office repair tools and checked all drivers (graphics, etc.) are up to date.
Thanks!