I know there have been logical explanations to tie this game to 1 and 3, but do you think that's really the case? or at very least, do you think that was really the developers original intention?
It just doesn't really seem like the case to me... There's not a single mention of the events of SH1. No mention of a single character, location, anything. I mean, sure, there's some vague references to occultism, but nothing that seems like it's specifically referencing the cult of SH1. To me, it seems more like a subtle nod to the first game than anything. I really think this game was developed as a separate universe. Just an alternate take on the core ideas of SH1: Person searching for a lost loved one in a place where elements of the subconscious can come to life. A mysterious plot that the player must piece together without being the story outright.
What do you guys think?

Same location different characters, SH2 is connected to SH4 that is connected to SH3 that is connected to SH

Why wouldn't it be?

It has the Seal of Metatron, meaning Alessa was definitely there.

They are most definitely connected.

The very reason the events of SH2 are even possible are a direct consequence of the events in SH1.

This basically sums up it completely in the most simple way.

There's no doubt it's part of the canon as far as I'm concerned.

It is related to the first and third games, but only indirectly, and the connections are not really all that meaningful. You have Frank Sunderland and Walter Sullivan as the two visible ties to Silent Hill 4, which itself only has thin connections to the Alessa story, and those two characters are intentional references to the second game. And, as per the trend of later and inferior titles, neither of these characters are actually relevant to, or meaningfully build upon, anything in the game it references.

What makes the second game the best game is that it stands entirely on its own merits, it's a significant part of the canon, but does not rely on any of that canon to construct its scenario.

TBH, because of later sequels, we tend to forget that the vast majority of the mythology and religion of the Order didn't exist in the series until Silent Hill 3. As important as the cult is to the original Silent Hill, it actually does not explain much of anything related to it, and virtually all of that information comes at the very end. For 95 percent of the game, you really don't have any clue what's really going on.

I wouldn't be surprised if the original intent was to have it be something separate kind of like how Twilight Zone or Final Fantasy do things. At this point though it's firmly connected to Silent Hill 4 which is firmly connected to 1 and 3 so there's no doubt it's part of the same continuity at this point.