Can a handheld emulate Switch, PS3, or Wii U?

Only the most powerful ones, and only partway. Upper-tier x86 PC handhelds and the strongest recent Android chips can run some 3DS, Wii U, and PS3 titles playably, and Switch emulation exists but is experimental, demanding, and highly title-dependent where it functions at all. Below that flagship tier, these systems sit in the "struggles" band. These are consensus bands from published testing that shift as emulators mature — check current compatibility for the specific games you care about, all of which you must legally own.