NO, all these taxes are computed separately on the 'base' wages reported on W-2.
Your figures for employee SS and Medicare taxes are correct, but Federal income tax is wrong. Federal income tax is computed using gross income including wages less some adjustments and deductions which can vary and usually depend on filing status, and then subtracting some credits which can vary. If a single person (who does not have a dependent child that qualifies for head-of-household status, and is not a recent widow/er permitted to file MFJ) with $100k wages takes the standard deduction for 2020 ($12400) and receives no credits, their tax will be $15103.50. For other status or if they have 'adjustments' (like a trad IRA and/or 'self'=nonpayroll contributions to an HSA, student loan interest, or alimony for most divorces before 2019) or itemized deductions that exceed the standard deduction (which is less common since TCJA) or credit(s), then the income tax will be different.
Note the employer also pays an equal amount of SS and Medicare tax on the same base. Because the employer considers that part of the cost of hiring you, even though it doesn't appear on W-2 and you don't even report it much less actually receive it, it could be considered stacked economically: the employer is spending $107750 of which they directly pay $7750 to the government, withhold another $7750 and pay it on your behalf, and withhold an estimated amount for income tax and pay that on your behalf. You actually receive ('take home') the remainder. If the withheld amounts for income tax prove to be more than needed when you file your 1040 the following spring, you get the excess back as a refund. (And if it's too little, you have to pay the difference; if it's much too little, you may have to pay a penalty also. If you file a correct W-4, and the employer doesn't massively screw up, that normally won't happen.)
In some cases, especially upper-middle-class like this, the employer also provides health insurance at no (visible) cost to you, but it adds to their compensation expense. And if you have a 401(k) or similar plan (see below), the employer often matches your contributions, or some of them, which also adds to their cost, but does not appear in your reported wages and does not affect your taxes. (Until you retire, when you will have more income and correspondingly more tax.)
But the 'simple' case above is changed the employer offers, and the employee uses, certain tax-advantaged benefits. In particular, a 401(k) plan (or possibly an alternative like 'SIMPLE') would be fairly common for someone earning that much in wages. In this case elective deferrals by the employee are excluded from the income subject to income tax, but not for SS and Medicare. Thus with a 5% deferral, a reasonably common election, SS and Medicare tax are still computed on $100k but income tax is computed on $95k -- less the adjustments, deductions, and credits as above. In contrast employer (not 'self') HSA contributions are excluded from both SS and Medicare, AND income tax.