I was beating my head against a wall trying to get my system to go to 4k 60hz mode -- but I finally found a solution (I think).
I'm running a Rpi5 with LibreELEC 12.1. Its HDMI port connects to a Yamaha RX-A740 receiver, which in turn connects to HDMI Port 2 on my Samsung UN75TU7000 TV. That port has "Input Signal Plus" enabled. The TV correctly detects the receiver on that port. However, the Kodi settings did not offer any 4K refresh rate higher than 30hz. Same in the Kodi Whitelist settings -- no 3480x2160 refresh rate above 30hz shown. I have the TV in "Movie" mode (with additional tweaks), which yields the best picture quality.
Today, I connected the Rpi5 HDMI port directly to the TV's HDMI Port 2. Immediately, the TV detected it as a "PC". When I opened the TV settings, the only modes offered were "Entertainment" and "Graphic" -- but I want "Movie" mode. Going back to Kodi, though, I now saw the 60hz option available -- so I whitelisted it and changed the refresh rate.
Then, I reconnected the Pi through the receiver, as per normal. The refresh rate stayed at 60hz, even across a boot. It disappeared as an option in the Whitelist settings, but that doesn't seem to have mattered. (Unless Kodi is showing 60hz, but really using 30hz....?)
Hope this helps someone in the same situation.