AT rifles were intended to fight light vehicles and weren't supposed to be analogs of AT grenade launchers.
The closest thing to AT grenade launchers in the soviet army during the war were cumulative hand grenades like RPG-43 or RPG-6. They were cheap and relatively easy to use compared to the same things of other armies, which is probably one of the reasons why soviet officials didn't bother getting AT launchers until they met Panzerfaust.
Wrong. The USSR was actively interested in new types of weapons back in the 30s. The USSR was generally quite innovative in this matter. The problem is that the economy could not implement these ideas.
In 1931, the USSR tested a 65-mm
"jet gun", created in the Gas-Dynamic Laboratory by its chief, B.S. Petropavlovsky (yes, this is the famous laboratory in which the "Katyusha" was created). Its design contained a number of promising elements: the use of light alloys, a shoulder launch from a long tubular guide, an electric igniter for a solid-propellant rocket engine, a shield to protect the shooter from powder gases.
But there were still many problems to be solved in order to achieve reliability from rockets and, most importantly, accuracy sufficient to defeat a single small target. However, after the death of Petropavlovsky in 1933, this development was not continued.
In the 1930s, Kurchevskys recoilless guns were also created, the problem is that they did not use the cumulative effect in ammunition, but used kinetic energy.
There is also a problem in the chemical industry, for HEAT ammunition RDX is needed, only after the war was it mass-produced.
But the experiments continued, screw-type AT grenades were created: VPGS-41, new AT rifle grenades were created in 1942, 1943, VKG-40 in 1944 (this is a big story)
The best were the RPG-43 and RPG-6 anti-tank grenades. Experiments continued, but starting in 1944 Germany became the main supplier of grenade launchers for the USSR. But this did not really matter much, since the troops had a huge amount of artillery. Interesting fact: during the Battle of Berlin, one of the 4,000-man infantry brigades had 3,000 Panzerfaust.