Current tenant, soon to be landlord

Question:

I live in CA (LA county) and am currently renting. My current 9-month lease ends September 30. I bought a multi-family unit and close Aug 6. Tenants are coming in place with that property, and have lived there longer than a year. I used the VA loan and must occupy the property as my primary residence within 60 days of closing (Oct 6th). I plan to give them a “no fault, just cause” notice, giving them 60 days to leave the property. This overlaps with my lease by a week after expiration. I talked to my landlord and she said I could have a 4 month extension (through Jan 31) or opt to leave Sep 30. Her logic is trying to find a tenant during the holiday season can be harder.

What are my options to proceed?

Do I rent an AirBnb for a week? Or do I have rights as a tenant? Thanks.