Will I still be taxed at the normal 401K disbursement rate even though I used it pay my 2023 tax bill?

[edxsanchez]

Used 401K disbursement to help pay my last years tax bill.  

[DoninGA]

Using the distribution from a 401(k) to pay federal taxes owed is not an exception to the 10% early distribution penalty.

The amount distributed is entered on your tax return as ordinary income. The early distribution penalty will be entered on your tax return as a tax liability.

[MinhT1]

Yes. The 401(k) distribution will be taxed at your marginal tax rate,

Paying your tax bill isn't an exemption to the 10% early distribution penalty, so if you're younger than 59 1/2, you'll have to pay the penalty on top of income taxes on the distribution.

See this IRS document.