Few in the State Department or beyond had or even knew of Mrs. Clinton’s personal email address or of the private server, they said. Those who did not instead relied on her aides to convey messages to her — from personal wishes to urgent matters — for the most part using their state.gov addresses.

Mr. Sullivan was known as a principal conduit to the secretary. One career diplomat who served as an ambassador and who worked closely with Mrs. Clinton’s core staff at the time said that he did not have her email address and that if he needed to reach her, he went through Mr. Sullivan.

The official said that career diplomats knew the rules about not discussing classified information on what is known as the low side — the department’s email system — instead of on the high side, which is the separate classified system that diplomats and department officials use for secret communications.

At least 21 other emails that the State Department has made public so far from Mrs. Clinton’s server also include information now upgraded to “secret,” including the one about the drone strike that punctuated Mr. Kerry’s visit.

Also on the server was an 11-page document with the minutes of a meeting that the previous secretary of state, Condoleezza Rice, had with Israeli and Palestinian negotiators in 2008. The minutes, written by the Palestinians, were leaked to the network Al Jazeera in 2011 and broadcast as a documentary called “The Palestine Papers.”

Both Ms. Abedin and Mr. Sullivan forwarded the document to Mrs. Clinton. Although the minutes were not an American document and remain published on Al Jazeera’s website, the document has nonetheless been upgraded by the State Department as “secret” because of its discussion of sensitive American diplomacy.

The State Department has repeatedly emphasized that the decisions to “upgrade” emails as part of releasing them now did not reflect a judgment on the classification of the information at the time. Nevertheless, the officials said that “secret” and “top secret” classifications underscored the sensitivity of information that passed through Mrs. Clinton’s server.