In the US, there is only one labor law that is different for execs and high paid employees and that is overtime rules. Fiduciary duty does govern how a director or officer behaves while in the role, loyalty, no self-dealing, no stealing corporate opportunities etc. It doesn't oblige them to stay or dictate how they must leave.

In US and English law, "specific performance", so a court ordering you to do what you promised, isn't available for personal service contracts. In the US that's reinforced by the 13th Amendment's ban on involuntary servitude. So even if a CEO signed a contract promising 6 months notice and a smooth handover, the company can't make them do it, they can only enforce any financial penalties that are contracted.

I have never heard of this. Do you mind sharing some examples?

I'd never heard of this. It turns out it is very rare for publicly traded companies [1]. In these cases, I would guess it comes down to contract terms. But again, it's not as though the law would compel an individual to continue working at a company. It would just come down to what the contracts say, and, potentially, how the courts interpret those contracts in the event of a lawsuit.

[1] Examples I found: Worksport Ltd., Exicure, Inc., Rainmaker Worldwide Inc., and Acorn Energy, Inc.

it simply works, that's how you optimise tax on million+ sums, do you think ceo-s pay taxes on par with regular workers?

A contractor CEO? I know it is extremely common for directors to be contractors for tax reasons.