Russia will not run out of ammunition, this would have never happened as there is a baseline amount being produced.
That being said, Russia is facing a shortage.
We've seen on the front within the past few weeks evidence of shell rationing, with limits being imposed on artillery units.
This is reinforced by the fact that tanks are now being used in artillery roles.
Even with limits, Russian artillery is still having an impact in places like Bakhmut, the only route left being shelled day and night, but shelling intensity has declined.