The incidence of taxation (which party bears the burden of the tax, irrespective of who 'pays' it) is widely studied. As it relates to payroll taxes (paid by the employer) and income taxes (paid by the employee) most research finds that employees bear most (but not all) of the burden. This is the opposite of your claim.
Employees get taxed when they spend money by being consumers. Sales taxes and VAT are their tax burden. But income taxes of the employees are the burden of the employer. It's employer who has to fork that money because otherwise he wouldn't be able to pay enough so that the employee agrees to work.
https://www.sciencedirect.com/science/article/abs/pii/S00472...
Higher taxes cause gross pay to raise.
There's evidence that increasing cost of operation of corporations through taxation is not fully born by workers. It falls in large part on the owners and landlords (who were omited in earlier works on income tax incidence).
https://www.google.com/url?sa=t&source=web&rct=j&opi=8997844...
Debunking your claim:
> While in practice employers know exactly for how little money (in hand) you are willing to work and in absence of income taxes would just pay this much less so that your money in hand is the same.
I exaggerated my claim to draw attention to the fact that it's not like many people believe, that income tax burden lands fully on the worker.
While my claim sound proposterous the opposite claim that is also false (maybe even equally so) rarely ever raises an eyebrow, which I think is very telling.