Would it serve the attorney’s case to the public if he disclosed that it was not a search warrant but an arrest warrant?
No, it would not.
I have been on plenty of both search and arrest warrants with the feds. They have checklists for checklists regarding procedure for the warrants. If it had been a search warrant, she would have been left a copy of the return and the inventory. The servers would have at least four copies and they always have another agent or supervisor making sure the warrant was posted or presented properly.
Despite what you posted, you're not sure and are just guessing.