You'll have to check the manual for your particular equipment. e.g. the EOS C500 Mark II appears to only output at most 1080p signals over HDMI (see page 141; chapter 6; Video Output Configuration).
For the EOS C70 (page 127; chapter 6; Video Output Configuration), it appears that both DCI 4K and UHD can go out over HDMI.
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Ricky
Camera: EOS R5 II, RF 50mm f/1.2L, RF 135mm f/1.8L
Lighting: Profoto Lights & Modifiers
