Can anyone tell what this sheathing is from a 2005 build in a cold climate?

That greyish pressed stuff is wood fiberboard sheathing, and yes, it was still pretty common in the early 2000s in a lot of the Midwest. I ran into it on my own garage and again on a couple of remodels around that era. It's made from wood fibers pressed together with a wax or asphalt binder, and it does have a bit of insulating value, which is why some builders liked it. The partial red stamp you found was probaly the manufacturer's grade mark, those were printed right on the panels but they fade and flake off fast once they see any moisture. Here's the honest answer on structure: fiberboard has almost no racking strength. It'll give your siding something to nail to and it adds a thin insulation layer, but it isn't doing the structural work plywood or OSB would do. The trick is that a house framed like yours almost always has diagonal bracing somewhere to take that job. On a 2005 build that's ussually metal strap bracing set into the corners, or occasionally let-in wooden braces, sometimes covered by the sheathing itself. If your house has stood square through twenty Minnesota winters with no doors sticking or cracks over the corners, the bracing is almost certainly doing its job. On moisture, it's a mixed bag. Dry, it's fine and it can actually handle minor wetting without falling apart. But once it gets repeatedly soaked, say from a flashing leak, bad gutter overflow, or splash-back at the bottom courses, it swells, softens, and loses whatever nail-holding ability it had. The crumbly edge you found is typical right where siding was removed, since that spot got wet during the work. Behind intact siding with a housewrap over it, it's usually in much better shape than it looks from the exposed edge.

What I'd do is pull a few more boards at diffrent spots, especally under windows, at inside corners, and near grade, and press a screwdriver gently into the board. Soft and spongy means trouble, firm means leave it alone. And check the corners for those metal straps so you know the bracing story before you start pulling more siding.

This sounds a lot like what's behind the siding on my old rental, same crumbly grey stuff. When we rescreened the porch wall I poked around and it was fine everywhere except right by the hose spigot, where years of splashing turned it into mush about two boards wide. Never spread past there though, so the dry spots really did hold up.

If I ever get around to redoing the siding, is it normal to just pull this stuff off and put regular wall panels up instead, or do people leave it and go over it?

Ha, that stuff takes me back. We used to call it celotex or buffalo board depending on where you were, and half the tract houses around here in the 70s and 80s had it. You want to know the real gotcha, check how the siding nails are holding. Old fiberboard is notorious for letting fasteners work loose, so boards sag and gaps open up at the seams even when the panel itself is still solid. If your warped siding came off easy and the nails slid right out of the wall, that's your clue. And when you do replace those boards, nail into the studs, not just the sheathing. Ask me how I learned that one.

Update: took the nail-holding tip and went around the outside giving the siding a little tug. Most of it feels solid, but the boards near the south corner have a bit of give, like the nails aren't biting. If fiberboard lets fasteners work loose, is the fix just pulling those and re-nailing into the studs, or do you need to back it with something? Also checked near our spigot after reading about the mush spot and mine's dry so far.