I mean, Europe's got something like 7 times the economy of Russia. And two European countries also have nukes and are on the UN permanent security council. If the sanctions against Russia weren't enough to stop the war, this winter is unlikely to be bad enough to stop Europen support of Ukraine.
Conversely, if Russia finds that it can wield its fuel as a weapon capable of destroying Europe by either riots or total economic collapse, then Europe automatically has an existential threat that only ends when Russia can no longer play that card.
And America will do what serves American interests, not necessarily what serves European interests, and they're not threatened by Russia cutting off its gas exports.
But it makes sense from their point of view. The only reason to export to the West is to swap for real goods and services from the West. Since the West isn’t selling anything to Russia there’s little economic reason for Russia to sell anything to the West.
Russia has its own floating rate currency. It has no need of our promises.
I explained why it isn't their source of income. They have their own currency with a floating exchange rate. Therefore what you think is their 'source of income' isn't. The FX system means that a Russian exporters 'source of income' (that which they use to pay their staff and suppliers) is the expenditure of the Russian importer, or the generosity of the Russian government sector - primarily the Bank of Russia. [0]
In local currency terms it is the Bank of Russia buying the gas, not the EU. That maintains the rouble monetary circulation in Russia, countering the drain to Rouble net savings and taxation.
[0]: https://new-wayland.com/blog/how-russian-gas-is-paid-for/
"Size" of economy is not a real metrics.
You can have a huge-ass economy based on providing high-margin services, but it would be worthless if it is not sustainable.
On the other hand, take Russia that does not really do much of global market high-margin services economy, but has sustainable enough industries.
As for problems getting anything, they cant even source potatoes for something as basic as fries.
That doesn't mean their interests are the same as mine.
I'm not ukrainian, or russian, whatever the outcome of the conflict won't really affect my country unless we go out of our way to involve ourselves in it.
If staying out of it results in cheaper gas at the pump for me, then that's what we should do.