W4 completed incorrectly and how much additional taxes should I have withheld?

I don't think I completed the W4 correctly for new part-time job.  I'm married filing jointly and both of us are working.  Just started a part-time job with an estimated gross pay of $39,600 for remaining 2022.  My total income for 2022 from other sources is $309,402 (excluding income from new part-time job).   I noticed my first paystub only had $2.48 withheld for federal taxes...obviously this is incorrect and it needs to be greater.  My spouse's estimated income for this year will be $280K-$290K.   In order to not get killed on having to pay additional fed taxes at year's end.  How much more should I have withheld from current part-time job?  10% of gross per paycheck?  I get paid semi-monthly.

Thank you.