> America could at least try to engage Russia with submarine warfare and long range missiles, but what could Canada do themselves, muster a few hundred native locals armed with century old rifles?
Canada is already a substantial component of NATO anti-submarine warfare. Canada is involved in patrolling and has sea and air resources to do just that, and is in the process to acquire more ships for that role.
Canada has about 18 maritime patrol aircraft, while USA has about 60, mostly in the coast guard, and that depends on tasking (some are listed as search and rescue which isn't the same) and the capability to drastically increase that amount by refitting/sacrificing our huge fleet of transport aircraft.
You may have consumed some propaganda. Canada's military forces are well respected everywhere they have ever been deployed. In WW2 they were considered horrifically brutal to german soldiers and treated as a serious threat. In the GWOT, their technical competence and marksmanship was admired. They have a formidable air force, that would be effective at blunting Russian aerial incursions. Canada has spent more effort and resources building up Arctic capability than the US has.
Canada's biggest military difficulties have been weirdly inefficient procurement. They waffle back and forth on stuff that needs commitments.
> If Russia announces they are going to be drilling oil in arctic waters that are nominally Canada's, and declares their annexation of this territory a fiat accompli, what is Canada's move?
Russia does not have the power projection necessary to accomplish this. Canada alone could prevent this. How do they protect their drilling infrastructure on Canada's border when they cannot protect their infrastructure all over their country? How do they protect their oil in shipment from Canadian raids? Russia is so low on some capabilities that they cannot defend against air attack. Russia barely had power projection to do those things when it was the USSR and was actively managing and manning a real fleet. Their blue water navy is in shambles. Their flagship on the black sea was killed by (supposedly) two anti-ship missiles despite having a multilayered Anti-missile defense system that should have been perfectly effective against such a threat. Such systems were always considered worthy in the cold war. That means either those systems don't work as advertised, those systems have a serious and known vulnerability that makes them useless, or the flagship of a Russian fleet was in an active war zone with most of it's systems degraded or nonfunctional. That's pretty horrifying.
The biggest lesson people should take from the Russia Ukraine thing is that things don't have to make sense. Sometimes hundreds of thousands die because a few people in a few places were utter morons and did irrational things and everyone just awkwardly stood by and let it happen.