Yes, the Elgato Game Capture 4K X is compatible with the Xbox Series X.
4K X is Elgato's officially recommended capture card for Xbox Series X, and its HDMI 2.1 input matches Series X's HDMI 2.1 output -- supports the console's full 4K144 passthrough/capture range with no setup beyond plugging it in (Xbox does not enable HDCP by default the way PS5 does, per Elgato's own HDCP article).
“Switch 2, PlayStation 5, PlayStation 5 Pro, Xbox Series X, PC”
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Confidence: high confidence