Sadly same result! Just flashes for a moment then gone.
I'm betting there's some dependency missing that I can't pinpoint because all my PCs have whatever it is that it needs since I use them all for my work...
I did notice once way back that it might be throwing an error code before instantly closing that you could potentially screenshot by spamming alt + printscreen while it opens. If you manage to capture that, it would be a great help, but also I do NOT expect you to go that far for me. I will continue to debug and try to reproduce the issue on my end! You've already helped a ton so thank you so much for that!
So I finally managed to reproduce the issue but the fix I found was still installing the .NET SDK linked in the install instructions. Once I installed .NET on the PC that it was crashing on as you described, it started working normally.
Beyond that I haven't been able to find any other reason it would crash or any potential fixes yet.
I'll leave the link to the download here just to be extra sure you got the right thing but if this didn't fix it on your end then the mystery continues to be mysterious :(
That might be it!
I found one of my PCs with 22H2 and it is indeed crashing as you described where all of mine with 23H2 work as intended!
I'm looking into how to fix this now, fingers crossed there's something I can do about it on my end. I'm going to update the prerequisites on the page in the meanwhile.