The Overwatch 2 mode in which teams control a robot that pushes blockades is Push.
Push is an objective mode built around a large robot positioned near the center of a symmetrical map. Teams fight to gain control of the robot, which then moves a barricade toward the opposing team's end of the map. The robot advances when a teammate is nearby and stops when opponents contest the area.
Although Push resembles Escort because an objective travels along a route, it is not a one-way attack-and-defense mode. Either team can take control and reverse the direction of progress. This creates a tug-of-war: a team can recover from an early disadvantage by winning later fights and pushing the robot farther toward the enemy side.
The team that moves its barricade the farthest before time expires wins, with a full push to the opponent's endpoint also ending the contest. Control is different because teams capture a shared point, Flashpoint rotates among several capture points, and Clash uses a sequence of objectives. Push was introduced with Overwatch 2 rather than the original 2016 game.