I'm beyond impressed they found enough working T-62s. I expect there's an interesting story behind how/why that happened(?)

As I remember, it was intended to match up against the US M60 'Patton' MBT. Those two were examples of attempts to add enough maneuverability to heavyweight tanks so there wasn't much reason for lightweight ones.

What's next - the T34s from Victory Day parades?

I suspect the point of the T-62s is to force the Ukrainians to expend ammo (apparently the Ukrainians have received a third of the US Javelin stockpile). T-34s, if they use them, the same - and it'd be a shame to destroy those pieces of history. But I don't think the Russians care about that.