I agree.

However, I wish our culture considered it rude to just walk up to someone in the middle of deep work and ask them something - unless it’s really important and time critical. It could be a simple as sending a message first “free for a quick chat?”

My counterpoint would be that before the widespread availability of chat and things like that, it was considered perfectly normal in most workplaces to swing by someone's desk. The modern obsession with "deep work" in some circles is mostly a modern invention. (At least in places that didn't commonly have offices where you could open or shut the door as a signal.)

I should have been more explicit but it does indeed depend on the context. If I’m in the middle of something I will acknowledge the person and defer the question until I’m done politely. But I won’t drop everything and context for ad-hoc stuff.

I agree, though I certainly will finish my thought, typing a sentence or two, before stopping and saying something like "I'm sorry, what were you asking?"

I'd be considered 'young' and would think it at least aloof so I don't think its your old-fashionedness.

There used to be an old-fashioned, well-known hand-signal for this situation. You pause long enough to hold up one finger for a second or two, then return to what you were doing. The polite would then poke around or sit down or return in a half-minute or minute to see if you'd paused. The impolite would get barked at.