Congressman Paul Mitchell sues Michigan Governor Whitmer as a private citizen over "unreasonable emergency actions". Currently executive orders can be issued without legislative oversight. It is argued on one side that the power to issue executive orders is not extendable past 28 days and on the other side it is believed that EO's can continue to be issued without legislative approval. The video states there are lot of things in the lawsuit of which most won't stick but that some of the essential pieces may (I haven't seen the lawsuit to know anything about it). The legislature also approved taking legal action but hasn't done so yet. According to the video, legislature doesn't plan on filing anything in the next couple of weeks (I suspect that may change).
This is part of a broader defining of where executives order power (essential to protect the health and safety of people) is needed and when it should end (executive overreach that limits constitutional rights). At present the law doesn't appear to clearly define for all involved parties involved when an emergency actually ends and elected officials are part of the process again. It is suspected that there will be increasing pressure to curb executive powers as immediate risks to health and safety subside. While this seems extraordinary, the balance between legislative, executive and judicial has always been in flux. Novel situations seem to bring up a lot of unanswered questions and in turn challenges.
Michigan Court of Appeals indicated in a previous case that the state was within its rights at that time. Continued challenges and risk abatement may end up changing some of those rulings. HERE