Thanks@kanchababu! After reading the Q&A content pasted below (link attached), I had to set up an appointment with Immi. Officer to be 100% that my H4 spouse can work on TPS EAD without any consequence for future immigration benefits. Please see yellow highlight - although not directed to H4, it is generic enough and can be easily inferred for the purpose of H4 or F2:
1. Can someone with a non-immigrant status (e.g. F-1, B-2, etc.) apply for TPS? If so, will having or using a TPS-related EAD affect his or her other status?
Yes, a person with F-1, B-2, or any other nonimmigrant status may apply for and receive TPS. The individual can continue to hold both statuses, as long as he or she remains eligible for both. For example, if an F-1 (student) applies for and obtains TPS, but he or she continues to abide by all of the F-1 eligibility requirements, he/she can continue to maintain F-1 status and simultaneously hold TPS. Any individual who applies for and is granted TPS must continue to comply with the separate eligibility requirements of all other statuses (e.g., F-1, H-1B) that he or she seeks to maintain.
It is up to the individual to know and understand the requirements of all statuses he/she holds or is seeking to obtain and/or maintain. Receiving TPS or a TPS-related EAD does not alter any
rules limiting employment for certain nonimmigrants, such as F-1 students or
B-2 visitors. Before someone holding both nonimmigrant status and TPS chooses
to work using a TPS-related EAD, he or she should carefully consider whether
that employment could violate the terms of the nonimmigrant status, potentially
resulting in violation of the nonimmigrant status. F-1 students who are
considering working on a TPS- related EAD may want to talk with their
Designated School Official (DSO) and/or an immigration attorney to discuss how
employment could affect their F-1 status. We note that students who are
experiencing severe economic hardship as a result of unforeseen circumstances
may follow the usual process to request off-campus employment authorization due
to the hardship by filing an I-765, Application for Employment Authorization.
Recognizing the effects of the earthquakes in Nepal, USCIS has announced that
it will work to expedite the adjudication and approval, where possible, of
requests for off-campus employment authorization for F-1 students from Nepal
experiencing severe economic hardship.