Okay, so here is the President’s proclamation of the national emergency:
https://www.whitehouse.gov/presidential-actions/proclamation-declaring-national-emergency-concerning-novel-coronavirus-disease-covid-19-outbreak/
After reading it, I find that there is nothing stated that includes the suspension of any rights assigned to individuals in the Bill of Rights. Are those suspensions supposed to be stated in the emergency declaration? If so, well, they aren’t there. If not, then we are subject to the whims and interpretations of the emergency declaration by the various state officials, no?
In this case, the relevant order is the one issued by Gov. Abbott, no the one issued by Trump.
If it follows the typical pattern, Abbott has issued quite a few orders. In Maine, a few of the governor’s order say violation is a Class E crime (that “Class E” thing is epressed in maine law, your state will vary on terminology).
Enforcement is via the usual path: cops, DA, court.
Courts typically use weasel words to explain that the constitution is still in effect, even though it isn’t.