My wife H1b maxed out on 6/1/23.
We filed her change of status to H4 before i94 expiry along with my h1b extension.
Uscis approved everything but the start date in her h4 approval notice and i94 is 7/10/23.
Is she allowed to stay in USA provided H4 approval & i94 starts in a future date.
If the H4 is approved with I-94, it should be okay however typically USCIS will approve with no gap. In your case it seems like her start date on H4 is same as your H1B EOS approval and it may be that the adjudicating office didn’t pay attention to her H1B expiry date.
Talk to your immigration lawyer and get a second opinion.