I’m guessing this, but would bet I’m right… but the Kaytusha is the representative piece for the Soviet SPA. That’s what I use it for and the SU-76 for the TD.
I certainly see the Katyusha as an iconic piece of Soviet WWII military hardware. It was self-propelled (mounted on trucks, I believe) and it was used in an artillery role, so it fits the general definition of SPA even though it was a rocket weapon rather than conventional tube artillery. To me, its unusual nature is part of what makes it such a distinctive, nationally-identifiable weapon. And the nickname “Stalin Organ”, inspired by its intimidating whoooshing sound when it was fired, has a great ring to it.
A footnote about the Katyusha: it was an example of the pragmatic approach that the Russians took to waging the Second World War and getting the most possible use out of their limited industrial capacity. When heavy artillery shells are manufactured, a few of them will sometimes turn out to have defective shapes. This causes serious accuracy problems when such shells are fired from guns, so the normal practice is for defective shells to be rejected at the factory and discarded. The Russian practice was to redesignate these shells for use as Katyusha rocket warheads, so as not to let them go to waste. The Katyusha wasn’t a very accurate weapon – it was suited to mass area bombardment rather than precise artillery fire – so the addition of a mis-shaped warhead didn’t really matter very much.