Overlapping double HDHP coverage with HSA contribution

The last day at my previous job was on August 1st. I had an HDHP with an HSA and they contributed $500 to my HSA. I will have HDHP coverage until August 31st.

 

I will be starting at a new job on August 25th, and I will have HDHP coverage with another HSA account on day one of my new employment.

 

Will this concurrent, double HDHP coverage between August 25th and August 31st affect my ability to contribute to my new HSA? And will I still be able to contribute up to $4150 including any employer contributions provided I had an HDHP at my old job since January 1st 2024? (I don't have any dependent HDHP coverage)