I read the whole thread and I think that you asked your question in a way that is getting some strange responses. A question well posed is a question half answered. I understand that English likely isn't your first language. I'm not blaming your question, just saying that if we re-frame the question, it may help to get better answers.
EDIT: It seems that a few things were addressed by other posters after I left for a few hours before finishing my post.
I think the crux of the issue is that there is a major difference to geography and NHL vs other professional sports leagues that causes this "strangeness" you've identified. This is obvious to most Canadians and Americans because the understand the scale that the NHL operates on, but the scale might not be as obvious for someone in the EU.
I'll start with geography. Many Europeans (not sure if you're counted in that group) do not realize how big Canada and the USA are. Every Province in Canada is large enough to fit several if not half a dozen EU countries into it and also large enough to fit several US states into it. The comments about how you might not cheer for different teams in Austria doesn't fully answer something that might seem obvious to Canadians and Americans... the size disconnect of our countries.
Imagine this (or look at the maps):
Austria's land size - ~84,000 KM2
British Columbia land size (Province Canucks play in) - ~945,000 KM2 (11x Austria)
Alberta land size (Province Flames and Oilers play in) - ~662,000 KM2 (7x Austria)
Ontario's land size (Province Senators and Leafs play in) - ~ 1.076 million KM2
California land size (State that Sharks, Kings and Ducks play in) - ~ 404,000 KM2 (4x Austria)
Florida land size (State that Bolts and Panthers play in) - ~ 170,000 KM2 (2x Austria)
New York State land size ~ 141,000 KM2 (Where Sabres, Isles and Rangers play)
Massachusetts land size ~ 27,340 KM2 (Where Bruins play)
New Jersey land size ~ ~19,050 KM2 (Where Devils play).
Now imagine that between Boston and Philadelphia, with a range of around 550KM, you have the following teams in that range: Bruins, Isles, Rangers, Devils and Flyers. Other than perhaps another small pocket in California, most other teams are 800-several thousand KM away from each other. This is a scale that might surprise many EU residents.
After that, we have the fact that most NHL rosters are made up of many different nationalities.
Breaking down each NHL team's roster by nationality: 2023–24 season opening rosters - The Win Column
Every team has multiple countries, so the fact that Vancouver, Calgary, Edmonton, Winnipeg, Toronto, Ottawa, Montreal etc. are all in Canada doesn't mean nationality wise they're "Canadian". The fact the team is located in Canada means only a physical regional attribute. Add in the differences of how other sports in the EU are organized, the NHL teams do not really have a nation type of attribute that is as possible in a landmass like the European Union. Population densities also vary wildly between NHL cities with significant (lack of) population variances if (arbitrarily) looking at 250KM in all directions from the city.
Winnipeg is maybe a million people total if looking at a 250KM radius around that city. Then there's huge differences in 250KM population between somewhere like Chicago, Toronto/Buffalo, Ottawa, Edmonton, Columbus, LA, New York etc.
Another point I didn't think get touched upon that much in previous posts, individual player investment/rivalries. As mentioned, NHL isn't nation separated like Olympics and international tournaments, so that doesn't work. But this discrepancy also perhaps adds to the segregation of fandom for many of the fanatical or casual fans as well. Think the ultras, but less physical violence and more philosophy/verbal.
You rarely have an NHL fan being a fan of multiple teams, especially rival teams. It's a lot more work to keep track of multiple teams and teams are actively working against each other in a conference system. So Calgary/Vancouver/Edmonton for instance, most fans will hope for their team to win, but either ignore the success of their rivals, or cheer for the failure of their rivals in the hopes that their team comes out on top (ie: More points in an 82 game season than rivals to have highest chance of playoffs). It's hard to have a "collective we of a country" if the success of the other teams in the same country often have a negative effect against your own team. This is not unique to Canada for the NHL, the same occurs in the USA as others have mentioned. If you invest in your team (ie: Calgary for me), then the investment of cheering for Vancouver/Edmonton will automatically be lower by default due to the NHL system in place.
Then to further complicate but clarify this process, many NHL fans are fans of specific players. For instance, I as a Calgary fan can be a rival of the Oilers, hate nearly all things Oilers, but be a fan of Connor McDavid. Similarities, but different. Like the squares vs rectangles saying (ie: all squares are rectangles, but not all rectangles are squares). Calgary fans can be a fan of a generational talent in McDavid and hopes he wins a ton of accolades and without being contradictory, hope that the Oilers do not perform well to be superior to the Flames (yes, I know it's sorta contradictory and dumb when the Oilers just were in the Finals and the Flames are crappy right now). In general, following more than one team is kinda exhausting and only fanatical fans will do this. Following players no longer on your team is also kinda exhausting, but not the same level as following an entire team. I believe many EU hockey fans would be fans of NHL teams where one of their star players on the world stage played. Some started that way and just stayed (ie: Finnish Kiprusoff fans sticking around as Flames fans after he retired). Others are active (ie: German fans and Oilers because Draisaitl)
What this meant in this years final, was that as a Flames fan there was an added bonus. In other years, I would perhaps just barely follow the highlights. This year, it was more personal and I followed the finals a lot more and watched the games from beginning to end vs barely touching highlights and scores.
The reason for this is that from a Flames perspective, there were several players that grew up in our system and played for us for many years that some Flames fans became attached to. So the fact that Bennett and Tkachuk spent so much time in our system (5+ years for both) and we were invested in seeing them succeed for so long caused us to have attachment to them. Lomberg as well as a feel good story, but he was only here a few years. This might have meant that our investment in seeing these players succeed caused us to also carry forward that success to hoping for the absolute pinnacle success an NHL player could accomplish. That is to win the Stanley cup. This spill over of player investment and then naturally turned to hoping for the Panthers to win from some of us Flames fans. Former Flames on the Oilers roster were like Kulak, Ryan and Stetcher. Most of which only spent a few years here (less than 3-4 seasons for each IIRC and lesser role players/not grew up in our development system with less attachment).
A similar thing happened when it was Vancouver vs Edmonton in the playoffs. Quite a few Flames fans hoped for Vancouver over Edmonton. Again, it was due to rivalry (even though much less of a rivalry emphasis in recent years, Battle of Alberta is still bigger than Calgary/Vancouver rivalry), but the biggest thing that may have trumped that indifference was that Calgary/Vancouver had swapped many players in the last few years and thus we had many crossover players for which many of us had somewhat of an emotional attachment to vs barely any attachment to for other teams. (ie key players like: Lindholm, Zadorov).
Keep also in mind that there are many different fans. Some are combinations of the above. Some are none of the above.
Sorry for all the words. Hopefully it was a little helpful in understanding this attribute of NHL fandom and realizing that it's not strange from a North American perspective, but I can completely understand why it's strange from an EU one.
