yes, but not everybody has to do deep work all the time.

for example, part of my job is to be available to colleagues for consultation. it might be something to which i can quickly respond "ticket or gtfo" or "busy right now, could you ask me again in 10-15 minutes?". But it could also require me immediate action (some production environment is failing).

As a company culture it is important to empower people to tell "not now", to educate people to only tell "not now" if you actually can't right now, and to train yourself to write "not now" without losing focus.

Managers should be looking on results of someone work not what you type or when. This is one of the things that piss me in the tech industry, Incompetent managers using tools like the end of year feedback, number of hours spent in office or culture fit to decide if someone is perfoming well.

managers who think they are kings are kind of the problem

If your managers mistrust you so much that they feel the need to check up on you like a child, switch company quickly.

I don't send anyone "be right back" messages -- I will set my IM status to unavailable if I intend to be unavailable.

Have a look at Gitlab's remote working guide for lots more insight on how they address this situation: https://about.gitlab.com/company/culture/all-remote/guide/

As if everyone isn’t anxious enough.

That way you can be responsive in scheduled times, and unresponsive in focus time.

This idea that people at work should always be available is not a good standard that we've set ourselves up in. If you're in support or some job then yeah, this model won't work for you. If you're coding then it makes a big difference.

Perhaps you are reinforcing poor behaviors that make people feel dependent on micromanagement.