How are professors able to multitask?

As in many situations, more novelty creates greater cognitive load, while non-novelty creates essentially no load. A teensy bit of interesting novelty is little cognitive load, but/and can be quite provocative, depending.

Since relatively experienced people have ... experienced many things... few seminar talks would present much that is radically new, even if it is new to novices. So, even if it is not somehow made explicit by the speaker or by the senior members of the audience, 90% or more of any talk will be a recapitulation of known things... Yes, it is understood that this is mostly necessary, to set a common context for discussion, and that there is not any genuine novelty there.

Also, there is a self-referential aspect to the premises of the question. Namely, the people one sees multi-tasking happily are the ones who can do it. Those who prefer mono-tasking will not be seen multi-tasking. So there's a "selection bias", as well.

And, for me, as for many relatively senior people, I/we have seen many things, and even superficially novel aspects of a seminar presentation may be echoes of things we thought about 30 years ago, etc. Not that there's not progress, but that there are questions that have been pending for decades, and preying on our minds, so (hoping that our minds are still working well) it is not burdensome to hear contemporary progress, but, rather, a happy event. But, in contrast, novices of course have no reference to related technicalities they reflected upon 30 years ago, etc.

And, apart from a greater accumulated experience of ideas and facts, I imagine that a vastly greater experience of coping with novelty and confusion gives a great advantage. E.g., if a smart kid has never in their life before been seriously confused, it is a disturbing experience. And this is a serious issue for very-smart kids in most environments. Similarly for very-smart kids in most undergrad environments. Even up to a point in graduate programs... but/and all the worse to soooo belatedly (after establishing habits that cannot accommodate for this) discover that high-level science (etc.) involves a constant rain of confusion and exceeding-parameters. (For me, this is entertaining, yes, but for those who think that people can control/understand everything easily, and not be confused, it is often deeply disquieting, I gather.)

Practice makes perfect.

The main issue of multitasking is what Paul Garrett described: being familiar with what is going on.

One important thing about multitasking is it is not doing something simultaneously, but sequentially, very fast, while skipping things that are not important. Human brain can't focus on several things at one time, but it can switch between an array of tasks in milliseconds, given enough practice. Professors usually become professors by doing a certain set of tasks for many years and getting very good and very fast at it so it may seem like they are almost doing multiple tasks simultaneously.

For many it is just a routine one follows subconsciously: a student starts speaking - pay attention; what they are saying is familiar - switch to the laptop until they finish because you already know what they will say next; someone walking, sitting down, standing up - 5 seconds to do something else; you spaced out thinking about something important (e.g. lunch) - pull out a universal question or a joke from up a very long sleeve.

It is also similar to reading: how to humans read and recognize so many letters almost instantly? Look at the first letter, the last, skip everything in the middle, repeat for a few words, guess the rest.

I'd like to offer a different interpretation of what you are seeing, along the line of Nate's comment:

The speaker says something that sparks the listener's interest, either because it sounds wrong, or because it relates to something they've been thinking about recently, or...

This triggers a new thought. They pull out their laptop to check with other things they've read before, or do some calculations, or ... generally do some research.

After a while, they come to some conclusion, either positive or negative, and talk to a neighbour as a sanity check.

In question time, they ask about the point they have been thinking about.

Overall, no multi-tasking needs to have taken place at all.