I think all HDMI cables 10 years ago were only HDMI 1.4. You need at least HDMI 2.0 to get the bandwidth for 4K.
HDMI 2.0 specification defined a new, more efficient signaling method, for speeds above 1.4b limits (10.2Gbps), to allow higher bandwidths (up to 18Gbps) over existing High Speed HDMI Wire Cables.
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hdmi.org
When you run the new cables, put in conduit. NEVER run an AV or internet cable that is not in conduit, and that includes speaker wires.