I come from a scientific background (not political \ legal) and seek to understand whether the governor (under that authority of the state of WI) has properly exercised state authority in a bid curb viral spreading.
There are 50 separate answers: here is the answer for Wisconsin, which you specifically asked about. The order is here: it cites the fact that
Section 323.12(4)(b) of the Wisconsin Statutes authorizes the Governor to issue "such orders as he or she deems necessary for the security of persons and property'' during an emergency.
The entire section says
(4) The governor may do all of the following during a state of emergency declared under s. 323.10:
(a) Declare priority of emergency management contracts over other contracts, allocate materials and facilities in his or her discretion, and take, use, and destroy, in the name of the state, private property for emergency management purposes. The governor shall keep records of that action. Those records shall be evidence of a claim against the state. The claim against the state shall be referred to the claims board under s. 16.007.
(b) Issue such orders as he or she deems necessary for the security of persons and property.
(c) Contract on behalf of the state with any person to provide, on a cost basis, equipment and services to be used to respond to a disaster or the imminent threat of a disaster.
(d) Suspend the provisions of any administrative rule if the strict compliance with that rule would prevent, hinder, or delay necessary actions to respond to the disaster.
(e) At his or her discretion, waive any fee required by the state for the replacement of a permit, license, approval, or other authorization for a person who resides or is headquartered in the area to which the governor's executive order under s. 323.10 applies and whose permit, license, approval, or other authorization is lost or destroyed in connection with the state of emergency.
Thus this is a matter of "security". The chapter does not define "security".
That order has expired. The state of emergency declaration has been renewed, but there is not yet a replacement mask order on his executive order's page. There are some media claims that the mask order was extended, such as this, which provides no evidence, so it is not clear whether there is any current order (the article also sketches legal issues with renewing the state of emergency). The mask order is only good under a valid state of emergency, which requires legislative approval for an extension (which has not happened).