I do genuinely believe that the West envisaged that Russia would collapse within a few months, as it dovetails nicely with the following points:

• Leftover anti-Russian propaganda from the Cold War, particularly with how the USSR collapsed due to internal crises; I would say it's mostly guaranteed that Western intellectuals took all the wrong lessons and interpretations from how and why the collapse occurred.
• A general belief in their own superiority (the garden vs the jungle), looking at examples of how sanctions in the past have affected and weakened other nations, thus believing that Russia would similarly collapse because, again, they took the wrong lesson from previous sanctions on weaker countries. The emphasis on how many sanctions there were, and their projected impact on the Russian economy (which failed to materialize) feels in retrospect feels like the geopolitical version of trying to create reality by pure insistence that reality is the way that you are describing it, and we see Israel doing the same in Palestine today by insisting that Hamas is on the verge of defeat, or has been defeated, when in reality the vast majority of Hamas' resources and fighters and tunnels are still intact.
• Additionally, a general belief in the superiority of their propaganda mechanisms and narratives that they could funnel into the Russian population, and indeed, propaganda is just about the only sphere remaining where the West has unquestioned superiority - though propaganda can only go so far to actually affect the world, so long as the general population is kept relatively happy (as the Russian population was and is, especially compared to Europe).
• The military preparation of Ukraine for 8 years to resist Russia. It's hard to say precisely what the people in charge of that program intended - was Ukraine supposed to be able to take on Russia's military alone (due to a critical misjudgement that Russia's military was weak), was Ukraine supposed to just hold out for a little while and wait for Russia to collapse, or was Ukraine not really ready yet but events had forced the US to goad Russia? - but you don't pour weapons and training into a country for years on end in the way that they did for Ukraine for no reason at all. Profit is a secondary benefit for the American Empire, there's always a guiding principle of weakening enemies first and foremost.
• Starting the war at the end of winter so that gas supplies potentially being shut off would not have too great an impact, because by the winter of 2022, Russia would surely have been internally overthrown by West-friendly liberals and the gas could be restarted; this reason might have been given to the Europeans by the Americans to assuage them, as obviously America not only doesn't care about Europe's supply of gas, it indeed actively benefits from it being shut off.
• The narrative that "Russia expected Ukraine to fall in a few weeks and now Putin is really pissed that it didn't, what a mad and incompetent dictator!" always felt a little... strange, and bitter, at least to me. It feels like a projection of the West's expectations onto Russia - they, in fact, are very angry that Russia didn't fall in a few weeks and are just expressing that anger by assigning the reverse to Putin instead.

Russia failed to collapse but Ukraine also didn't collapse. So it feels like we've been in the Plan B of both sides since the summer of 2022. Russia hoped that they wouldn't have to go this far and that Ukraine would surrender to their (pretty reasonable) terms, and was met with a West that was proudly saying "Haha! Putin and his top experts thought we WOULDN'T slam our hands on this boiling-hot stovetop, and keep them there, writhing in agony! Those utter fools, completely incapable of analysis!" So then Russia had to mobilize forces, and so did the West, and 2023 happened and now 2024 is too.