How can I adjust my W-2 reported income, which includes tips I have earned, by the amount I tipped out to other employees?

your w-2 is wrong and needs to be corrected. here's what the IRS says about tip-outs.

Do I have to report tip-outs that I pay to other employees?
No. You report to your employer only the amount of tips you
retain. However, you must maintain records of tip-outs with
your other tip income (cash tips, charged tips, split tips, tip
pool)

https://www.irs.gov/pub/irs-pdf/p3148.pdf 

this is from another thread from 2020 but it is incorrect in that it only supposed to be used for tip-outs from unreported tips which is not your situation:

1. After you enter your W-2 in TurboTax, you will the screen "Let's check for uncommon situations."
2. Select Unreported tips, then continue
3. On "Let's confirm your allocated tips from xxxx" select Yes or No, depending on whether your allocated tips are correct
4. On "Now let's enter your unreported tips," enter the amounts of Total tips that you paid out through tip-sharing

reporting tip-outs on unreported tips without a greater amount for unreported tips will likely get you an inquiry from the iRS 

if your employer will not correct the w-2 you'll likely be on the hook for those income taxes 

There is no legally correct procedure to report your tip-outs on your tax return.  When you report tips to your employer, you should only report the net amount you kept after tip sharing, not the gross amount, and your employer should only report as wages, the net amount you kept, not the gross amount before sharing.  

If you have accurate records, you may be able to get the employer to issue a corrected W-2.

Anything you do on your tax return is likely to get you a letter from the IRS, if your tax return does not match your W-2.   I am also not convinced the quoted procedure will work.  It seems to me that you would have to report a negative number as unreported tips, to try and reduce the taxable amount.  And I don't think that will work.

(Note that tips you received and reported to your employer should be included in your box 1 wages along with your hourly wage.  The box 8 allocated tips are tips that were paid directly to the employer that the employer must allocate to the employees.  Adding additional unreported tips will increase your taxable income, not decrease it.)

You can also try entering a corrected W-2.  After typing in your W-2, there is a list of special circumstances, and I think there is a box for "my W-2 is incorrect".  Turbotax will allow you to enter what you believe to be the correct figures, and the program will include a "substitute W-2" form with your tax return indicating you believe the W-2 is incorrect.  But you will most likely get a letter of investigation and you will have to prove your case.  Did you keep accurate daily records of your tips and the tip sharing?