I mean, sure you can reason about a portion of code on your screen but there is no way you could emulate anything without some visual support.
There is no way your short term memory could store the program and the variables. The human brain can barely remember 5 to 10 words for several seconds and you have no control on your long term memory.
So yes your brain can somehow emulate a computer if you give him a pen, a sheet of paper paper, time, and a lot of sugar. But that’s not because it’s functioning like a computer but rather because you learnt how a computer work.
The halting problem is about computable functions. Every real thing can at most solve computable functions — so for all practical purposes, a brain is a computer that has all the same limits.
That’s a common misconception. The brain is not like a computer. The brain can’t store and execute programs.