According to ISW, the Armed Forces of Ukraine entrenched themselves on the left bank of the Dnieper in the period from April 20 to 22. The size of the bridgehead and the forces supporting it are still unknown.
Russian milbloggers have provided enough geolocated footage and textual reports to confirm that Ukrainian forces have established positions in east (left) bank Kherson Oblast as of April 22 though not at what scale or with what intentions. Geolocated footage published by a Russian milblogger on April 22 shows that Ukrainian forces have established positions on the Dnipro River bank north of Oleshky (7km southwest of Kherson City) and advanced up to the northern outskirts of the settlement on the E97 highway, as well as west of Dachi (10km south of Kherson City).
Probably, the occupation of the bridgehead is part of the spring offensive announced by Ukraine.