What if you got another new I-94 (by using AP) with an expiration date earlier than that on the I-94 which came with H1 approval notice?
-When you leave US and provide the I-94 (e.g. H1 I-94), your h1 status or any non-immigration status is over (only if a non-immigrant is physically in US, he/she can have a non-immigration status). When you enter US with a non-immigration visa (e.g. H1 visa), you get a non-immigration status (I-94) again (e.g. H1). If you enter US again with AP, your status is parolee, not H1 or any non-immigration status.
If your status is H1 before you leave US and then, you return to US with AP, your status is parolee, but you have some benefits of the H1 holder such as you can continue to work for your previous/original employer who sponsored your H1 without using EAD, and you can reinstate your H1 status anytime by doing H1 extension or h1 transfer.
See:
Will the new I-94 (by using AP) overwrite the old one (with H1)?
Do we need to do anything to continue working using H1 when the new I-94 (by using AP) expires, while the old one (with H1) is still valid?
-Yes. You just need to do the H1 extension before the H1 approval notice expires or do H1 transfer any time before the H1 approval notice expires and thus, you will reinstate your H1 status.