It doesn't matter if a war is popular or not, they annexed 4 regions of Ukraine into Russia so they could sell the idea that they're defending Russia and anyone who doesn't want to fight is abandoning their country. That will make the mobilization pill a lot easier to swallow. Russia also doesn't have separatist groups to deal with and they have Central Asian immigrants to deal with all the tedious work so they could pretty much strip all the man power they need.

You're also stuck in the beginning of the war when Russian logistics were truly awful since they only brought enough supplies for 3 days, thinking they could YOLO run to Kyiv with out securing their flanks. They now have the logistical capabilities to get 40 to 50k soldiers across a river well being shelled relatively safely. We also haven't seen a significant number of Russian troops just giving up, weve just seen Ukrainian videos showing the ones that have. The battle of Mariupol alone led to 4000 Ukrainain pows, thats far more than how many Russians are in Ukrainian captivity.

That is also just not true, both Russia and Ukraine are Soviet armies and Russia still has tens of millions of AKs in storage. NATO maybe giving them guns which are 20% better but that doesn't matter since like you said, it's not the Napleonic Era where an extra shot per minute really matters.

At the end of the day, it's about who could bleed more and that's Russia.