My TPS (i821) application is pending but corresponding request for EAD is almost done. When I can start working with this EAD?

I have been waiting for work authorization since applying for Temporary Protected Status & employment authorization document (i821/i765). USCIS case status for EAD was recently updated & says they have ordered a new card for my receipt number (from i797C for i765) and will send it within 30 days. However, my TPS application is still pending since initial review. Case status (from i797C for i821) says fingerprint fee was accepted (over a month ago) & that the Nebraska service center is working on my case. - If I receive my EAD soon, without any further progress on my TPS application or its approval, can I use the card as valid work authorization? - Do I need both applications (i765 as well as i821) to be approved before being able to work in the case of such TPS/EAD requests?