"Do you both agree that total payroll taxes should be 12.4%?"
12.4% of what? 12.4% of $142,800 of your total compensation for 2021? No, there is no such limit.
For 2021, the total employee portion of Social Security taxes is limited to 6.2% of up to $142,800 of total compensation. The employer portion is separately limited to 6.2% of up to $142,800 of compensation earned at each separate employer. There is no combined limit for your employers.
12.4% is mentioned nowhere in the tax code (except for the self-employed, which you are not). The tax code specifies 6.2% for each individual (26 USC § 3101(a)) and 6.2% for each employer (26 USC § 3111(a)) . The amount that one of your employers must pay has nothing to do with what what the other of your employers must pay.
