If it ends up that the next Switch 2 isn't capable of offering a backwards compatibility solution with original Switch games, would that affect your decision in purchasing one?  

Unlikely to affect my own decision, but I think it would be pretty terrible to not have it.

There is no decision Nintendo could make that would make me not buy their next console outside of it not having their new games.

That said, would I be disappointed in no backwards compatibility? Yes, sure.

I'd buy Virtual Boy 2 if it had some exclusive Nintendo games though. 

Either way it’ll be a day 1 purchase for me. Having said that, I’ll be disappointed not to see backwards compatibility.

If the console is no backward compatible, i Purchase the new console late . I need to have at least 10 good games to justify buying a new console.
If Nintendo make performance or resolutions upgrades to old titles in the new console (Like Microsoft with xbox series in old games ) That will be great for consumers, and a way to keep the console with sales even if they dont have many games ready at launch. (Some new buyer could buy all Xenoblade games with performance upgrades or the Legend of Zelda games)

Nintendo Switch has sold 1 billion games. Nintendo would be fucking idiots if it wasn't BC. I alone have over 130 physical games for the system. Yes, it would influence my decision. A big selling point to me on PS5 is all my PS4 games work that I own.

So, at this point I was the first to choose "I won't buy". Let's see how many more.

I cant imagine a scenario where its not BC. It sounds like its gonna be a "Switch Pro" of sorts, not an entirely "new gen" console.

It would be a major oversight and missed opportunity if the successor was not backwards compatible.  Whereas I already have the games I want to play or collect on Switch, it would be an absolute travesty for a new Nintendo ecosystem adopter to not have the massive library of the Switch, available to them at launch.

That said, I have started over with every other Ninty system (with the exception of the GameCube/Wii), so the lack would not deter myself from a day 1 purchase.

It's an Anti-consumer move not to have it, but it won't affect my purchase directly. If the next system has 3D Mario, Super Smash Bros. 6, Luigi's Mansion 4, Xenoblade Chronicles 4, or Mario Kart 9 in the first 6 months, then I'll probably get it at least in the first year. Any of those by themselves is enough to get me seriously interested early on.
Nintendo software, like usual, is the driving force for me.