It's been few years since I have handled classified documents but as I remember the document is stored in an enveloped that has classified printed on the front and the classified level, Top Secret, Secret, etc is on front of the envelope. And I believe there is a warning not to open if you do not have the clearance. Also, there is control number for documents.
There is also a code that provides additional information on the document. That information code varies with agencies but all of the codes identify the source of the document. I don't remember all codes but there is one that indicates that the document is not for viewing by foreign nationals. Anther code indicates information collected from human sources, etc.
So without violating security, anyone can look at envelope and tell where it came from and usually a code that provides more information about the kind of information inside.
The Constitution, through the Fourth Amendment, protects people from unreasonable searches and seizures by the government. The Fourth Amendment, however, is not a guarantee against all searches and seizures, but only those that are deemed unreasonable under the law.
This search warrant is creation not unreasonable. The DOJ creations hundreds of search warrants a year, an none of them
As long as the search warrant has the correct address to be search and there is cause in the warrant for the search and items to seized, the warrant will stand. Search warrants do not require the probable cause that arrest warrants require. Search warrants only require reasonable information to support the
possibility that the evidence of illegality will be found.
The DOJ have created over 621 search warrants in 2021. Of those, 210 cases have come trial to. Of those cases not one search warrant has been found illegal. Of those 210 cases, there were been 36 pretrial hearing to dismiss evidence from searches. Of those only 7 dismissed any evidence from seizures.
The DOJ knows how to create search warrants and the FBI knows how to execute them. The chance of the Trump's defense team getting any evidence excluded is poor and the chance of getting all evidence excluding is about zero.