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The names are pretty clear and are about form factor. Desktop is something on top of a desk. Laptop is something on top of your lap. Hand-held is something you hold in your hand.
The steam deck is a hand-held game console - doesn’t matter what OS is it uses. It’s true that most stat tracking sites count it as “desktop” but not because it’s a desktop computer but because the user agent looks similar to desktop user agents.
If I install Android on a tower PC it doesn’t randomly become a smartphone even though all browser trackers would register it as a smartphone.
And Valve using a “typical desktop OS” on their handheld console doesn’t magically turn it into a desktop PC.
Desktop is a form factor not “software” and there are microwaves and refrigerators with “PC hardware” (in quotes, because it’s actually a pretty ill-defined term), but they still are not “Desktops” even is you install Fedora on your fridge.