Yes, brain surgeons are working class. They earn a lot because they actually produce a lot of value. If you suffer from a brain disease, getting surgery to fix it is probably one of the most valuable things you can get (depending on the severity, it will be the most valuable thing). Additionally, it requires a lot of skill.

Yes, what the hell do you think the word "working" is doing there?
If you're work for a living, you're working class. Even if you get paid a big salary, you're still a person who works a job for it.

They're upper class, which is part of the working class because they earn their money by their labor, aka working.

If they earn their money for simply owning things and collecting interest then they're not working class.

A brain surgeon makes money by working on brains and therefore is in the working class; the person that owns the hospital makes money by extracting rents from the brain surgeon and therefore is in the capitalist class.

Upper class and middle class don't necessarily correspond directly with those terms.

You can label different sections of the working class but on the scale of history and societies the only real divisions in society is between the class people who trade their labor for money and the class of people who earn money simply by virtue of having money.

The poorest Walmart employee and the richest doctor have more in common than the doctor and a person of inherited wealth. You'll interact with doctors and engineers many times a year in your community. While you'll probably never be in the same room as a wealthy person.

Laws that protect labor, provide social safety nets, provide for education, security, etc all benefit the Walmart worker and doctor. But they're completely worthless to the people who own their own security, pay for their own education and never have to worry about starving to death if they're unable to work.

We're seeing the wealthy taking control and deciding that they can save money by simply choosing to not support working people. After all, what are we going to do? Stop working for them?