You may be overthinking what you are doing for 2023 at least, since according to you, you will not start that job until later in November with only a few paychecks to go in 2023. For 2024, forget stressing over the not getting paid during school breaks, etc.-- what matters is how much you earn during the tax year from January to December, regardless of when you receive those paychecks.
https://www.irs.gov/individuals/tax-withholding-estimator
https://www.irs.gov/pub/irs-pdf/fw4.pdf
**Disclaimer: Every effort has been made to offer the most correct information possible. The poster disclaims any legal responsibility for the accuracy of the information that is contained in this post.**
