I sat next to my very first technical mentor for a few years, and he had no compunction about holding up a finger and saying "hang on" curtly when I'd start to ask something. If you all agree that it isn't rude in this context, I think that reaction can help. I do it myself occasionally and usually can keep about 80-90% of my flow.

Try doing that to your wife on work-from-home days at your own peril.

Wife nothing, try doing it to the exact same mentor who felt entitled to do it to you.

If my experience / observation is any guide, the result is utterly epic shitfit.

I have done that, and no explosions, nor any shitfits.

It depends on both the way you do that, and the way people talk to each other there (aka the culture).

Work with better people?

At my last job (less applicable now as I WFH), it was acceptable practice to give a "hold on" to everyone you'd run into on a daily basis. Maybe not the CEO, but the VP of Engineering would wait a sec if you needed to get something done Right There.