A month gap between my current job (academic H1b valid till 2026) to my new job (approved academic h1b petition)

I am currently on H1b (academic) with validity until 2026. However, I have decided to join a new job and my new I-797 (academic H1b) has also been approved through premium processing (filed by my new Employer). The start date mentioned in my new approved I-797 is from 15th November.
If I quit my current job on 15th October and take a break until 15th November., can I do that?
If not, then what are my legal options to take a month gap between two jobs like unpaid leave?
I would really appreciate it if you could please answer that. Due to the housing situation, I am in a tough position.
Please let me know if any more information is needed.

Thank You very much and looking forward to your advice on my situation.

Thank You