There even isn’t much panic about being caught on the street to be conscripted
Because Russia hasn't mobilized besides the "partial mobilization" in 2022. The question is why. One theory is that they don't need to. The other theory is that they can't. I live in the US and remember the Iraq war. In 2004 one of the biggest things going around was that Bush was going to start conscription.
But if he were to have attempted mobilization the support for the war in the US would have instantly collapsed so instead he tried various things to fill the ranks like using mercenaries, "backdoor drafts" via stoploss, activating national guard, etc. And in the end, let's be honest, the US lost both of Bush's wars.