797 Was valid for family and self unto Mar-2024 and living in USA.
New H1B amendment and extension approved from Oct-2023 to Sep-2026.
H4 Extension are not filled yet. Any issue?
Assuming it can be filled before Mar-2024.
No issue. It doesn’t hurt to wait and apply later prior to March 2024.
BTW: Did you use premium processing to do H1B amendment and extension? If so, I believe H4 would also been processed under PP if it was filed together with H1.