The shoot-down of Powers is a famous event in the history of modern military.
Did US stop using U-2 afterwards on USSR?
It is known that this event stimulated the US spy satellite program.
I think this is (partially) answered by Wikipedia
On 4 January 1961, the CIA U-2 reconnaissance effort, which was formerly known as CHALICE, was redesignated IDEALIST.104This program codeword by the end of the decade was being used to describe the U.S. reconnaissance along the Chinese coastline, while Taiwanese missions into the Chinese country would be known as the IDEALIST program105
Although Eisenhower refused to end the U-2 program, it was quickly overtaken by new technology, as satellite images replaced aerial photographs. state.gov
I don't see any evidence of U-2 flights over the Soviet Union or Russia, but absence of evidence is not evidence of absence.