Getting a second job for first-time home. Affects underwriting or no?

My first house is set to close/will be built in about 3 months, and I'm feeling anxious about savings. It's new construction. I showed my w2 income for the loan and qualified, and got conditional approval for a pathways loan (using gift money and grants for downpayment) and I think they will ask for paystubs in another month or so. I could really benefit from a second job right now to save more money, as I'm worried about moving costs/and other expenses and I Want to ensure I have more savings as a buffer. I was wondering if I take on a second job like Doordash or another w2/contractor job, if it will affect my loan? Or would it be better to open another checking account for the second job money - if so, would the underwriters know about it or request it, or would I be able to just not report it.

Any other tips on how to save extra?

I'm not really sure what is the best/smartest thing to do?