Welcome to the forum!
Oh gosh, I'm not very good with printing issues. Possibly the reason the one with the correct size is printed as if rotated, is because Inkscape's internal coordinate system uses the top-left corner for the 0,0 axis intersection. I might guess that your printer is aligning itself to that, which seems to rotate the image.
But I couldn't even guess why changing the page size corrects the rotation. Maybe being square gives the printer a choice (how/where to align the 0,0 center), and it chooses the correct one?? But that's a pretty wild guess.
Or maybe it's just some printer settings that need to be changed? At least that's something you can investigate.
Hopefully someone with more printer knowledge will answer soon.