I learned this lesson a few years back when I interviewed for the CTO role of a educational software company - the main part of the interview was preparing a presentation on how to launch a new product which I had to prepare and present to the management team.

That went very well and I was feeling pretty good.

Then the CEO had a quick chat and happened to ask me a very simple technical question and my brain would not work - I completely failed to do it even though it was trivial.

I think that's how I discovered that mental context switching is a real thing - I had spent a few hours preparing and giving a presentation and then when asked a simple technical question those parts of my brain were completely offline. I think the shock of not being able to do it had a big effect on me and I went to bits (possibly the first time I've ever done that).