The withdrawal is income, and it is added to your regular income in the usual way, and subject to the usual tax. The withholding is taken out by the government to make sure you aren't underwater too much when you file your taxes, it is not the tax you owe.
Assuming you are single, the withdrawal will be taxed partly at 22% and partly at 24%, plus the 10% penalty for early withdrawal, plus your state income tax (3-10% depending on your state).
Remember that moving into a new tax bracket does not subject all your income to the higher rate, just the amount that is over that next threshold. So for single individuals, and after taking off the $12,000 standard deduction; your first $10,000 of income is taxed at 10%, the next $30,000 is taxed at 12%, the next $45,000 is taxed at 22%, and 24% after that. So let's say $75K income minus 12K standard deduction is $63K, that will be taxed partly at 10, 12 and 22. If you add $25K of income, that's $100K, minus $12K for the standard deduction leaves $88K, so the withdrawal will be taxed mostly at 22% and a little bit at 24%.
https://taxfoundation.org/2020-tax-brackets/#brackets
