There were British and American bombing campaigns on German cities during World War II. Did the Soviets ever conduct any operations like this? If not, what were USSR bombers mostly used for?
Short answer is, no.
They did have bomber raids on Konigsberg and on Finland, but these raids were small with small effects. They were mainly nuisances or tactical in nature.
The Soviet Union simply didn't have the resources and ability to maintain a long range strategic bombing force while also maintaining the tactical aviation necessary to win the more immediate threat - the German forces on the ground.
Consider this: the Germany Army is advancing on you across a massive front with tons of armor and troops. You can choose to retool your factories to pump out 4 engine long range bombers to bomb German cities deep behind enemy lines. Or, you can pump out single and twin engine fighters and attack aicrcraft to shoot down enemy fighters and attack planes and then destroy enemy tanks and artillery.
Thus almost all Soviet aviation in WW2 was thus geared towards tactical engagements to either gain air superiority or in support of of operations on the ground