Not while performing in front of an audience, no, very, very little of that.
You know the trope of almost all students dreading going up in front of the class to solve a problem on the blackboard/whiteboard? A thing that I think I personally only actually did a countable-on-fingers number of times ever, and only in lower grades?
It's a trope for a reason, and it's because the vast majority of people do in fact hate having to get in front of an audience and perform. Hell, it's often a component of recurring nightmares.
It's like that but way worse because it's also far more high-stakes than that, the problems are far more complex, the point is explicitly for everyone in the audience to judge you and not just your assumption that they all are causing the stress, et c.
It's more like the stress from getting up at an open mic night, than any kind of stress I've ever actually encountered on the job. Even the dynamic in a meeting with clients where you have to diagram something out on a whiteboard or something is totally different—for one thing, you generally have people in there who are very much "on your side", and you don't have to worry if you misspell something that you're personally about to be/remain unemployed, or lose out on a huge raise, or whatever (nobody generally cares about minor mistakes on a whiteboard in an ordinary context, and maybe they don't in some interviews, but they do in others, and candidates worry they might in all of them).