Funny thing is that I grew up in Berlin and never noticed the Soviets occupying more than East Berlin, which, according to Yalta was their sector anyway. They TRIED to push the western Allies out with the blockade of West Berlin in 1948-49, but didn’t succeed.
What they tried several times though, was to disconnect East Berlin from the Allied status, first by handing it over to the East German government as their capital, then by having East German police insist that they could control Western Allied military and political representants at the Berlin Wall check points. This led to a show down with American and Soviet tanks facing each other at check point Charly.
Later there were attempts by the East German government to take over air traffic control over West Berlin, but the Western Allies told them to F+ck off and the attempt was not repeated.
Also, in the early 1950s, Honnecker, in his at this time role as the leader of the communist youth organisation FDJ, tried, with Ulbricht’s support, to have hundred thousands of East German communist teenagers to march into West Berlin to claim it for the East Germans, but the march got literally beaten back (with baton charges) by West Berlin police under Western Allied command. Honnecker and Ulbricht, who apparently pulled this stunt without asking Stalin, who was at this time in talks with the Americans (I think over Korea), were summoned to Moscow, where they had to undergo an interview without drinks being served.
Jan
Edit: Cleaned up typos