Do we need to apply for wifes H4 Extension?

[sawyer]

My wife's H4 expires August 2020 so does her I94 but my I797 and I94 expires September 2021. We both have a valid H1/H4 visa stamp till August 2021. We recently crossed the US POE and my wifes' I94 was extended to September 2021 with the H4 visa status on the I94. Do we still need to apply for my wifes' H4 extension via applying for the I539?
We have also applied for the H4EAD extension with the I94 extension we received for the period between Aug 2020 to Sept 2021. We are worried that this I539 extension might affect the H4EAD extension application.

Can anyone provide advice? Should we go forward and apply for the I539 extension?

[newacct]

No. Her current I-94 is until September 2021. She does not need to extend her status until then.