I’m no miltary expert, so I apologize if my views are unsound, but my impression is that Russia has, like, a gazillion tanks and a huge army.
Or are my views too Cold War and out-of-date?
Tanks aren't what they used to be, and Russia could never launch a successful attack against NATO, and the oceans, and the skies, they aren't even structured the way they used to be, they used to be built for attack, and of course Russia is incapable of protecting itself on it's other borders and from internal rebellion if it committed it's small military against NATO, or lost the bulk of it in war.
The general condition of the Russian Army is poor - most units would have been classed as Category 3 back in the Red Army days. That is not to say they would be a pushover, and they can certainly run rough-shod over Ukraine and possibly Poland. They can also put more effort into improving their situation, but they still have vast layers of tradition and institutional corruption blocking much progress.
Russian Air Force and Navy forces are in similar poor shape - most of the old Red Fleet is non-operational and rusting at peirs. They have some good ships still, and have built a few newer ones that are impressive, but their shipbuilding has fallen from its Soviet days and they actually have to get ships built in France (something the Red Fleet would never have done). Russian Air units have some good fighters but are lacking in fuel and spare parts - again, soemthing that could be addressed with effort, but expense and corruption seem to dog them at every turn when they try to improve things.
Do not take this as a dismissal of the Russian military. Some parts of it are quite good indeed. However, it is not the all-conquiering boogeyman some would have you beleive. It could easily defend Russian territory from all comers, and even make some inroads against its neighbors, but would not be able to defeat a united NATO in a European invasion, even in NATO's current weakened state.