My Chromecast Ultra ($54) HDMI supports 3840x2160 @ 60hz. The result is a beautiful picture and smooth stream experience. I love it. Yet, MY 8TH GEN INTEL i5 8400 W/UHD630 GRAPHICS WILL NOT SUPPORT 60HZ AT THAT RESOLUTION W/HDMI EVEN THOUGH IT COSTS SIGNIFICANTLY MORE! WHY?
First, do not be afraid to release the CAPS LOCK.
Second, you should get rid of the i5-8400 and run everything on your Chromecast Ultra.
Doc (not an Intel employee or contractor, just a customer)
Your processor supports both DisplayPort 1.2 (HBR2) output and HDMI 1.4 output. If the DisplayPort 1.2 output mode is used, the processor can support 4K@60Hz (SDR or HDR). If the HDMI 1.4 output mode is used, however, it can only support 4K@30Hz. Cheap motherboards will directly output a processor's HDMI 1.4 output stream. Good motherboards will use an LSPcon chip to convert a processor's DisplayPort 1.2 output stream(s) into a HDMI 2.0 output stream(s) and thus can support 4K@60Hz. If you are unable to get 4K@60Hz, then you have a cheap motherboard, plain and simple. If you are using a DisplayPort 1.2 output stream directly, use either a DisplayPort monitor or a dongle that converts to HDMI 2.0.
Wikipedia (https://en.wikipedia.org/wiki/DisplayPort and https://en.wikipedia.org/wiki/HDMI) provides a wealth of information regarding graphics capabilities. Intel's Graphics FAQ (https://www.intel.com/content/www/us/en/support/articles/000005529/graphics-drivers.html) provides information on the processor's graphics capabilities.