What is the HDMI refresh rate for Intel® UHD Graphics 630?

The specs say that it supports HDMI at 4096x2304@24-30Hz. Does that mean that it can support a lower resolution at a higher refresh rate? Also, if I use a DisplayPort to HDMI adapter does the refresh rate follow DisplayPort or HDMI?

The maximum refresh rate shown is the "pixel clock" rate. i.e. mathematically 4096 x 2304 = 9,453,568 pixels per frame and it can then put out 30 times that every second for approximately 300 million pixels per second. Is the maximum number of pixels that can be thrown per second.

If you have 1920 x 1080 pixels, which is 2,073,600, slightly under 1/4 of the full 4K resolution, then it should be capable of approximately 120Hz. From experience I can say that HDMI 1.4 definitely can handle 120Hz, so that fits well with theory.

DisplayPort and HDMI are also separate and work on separate protocols. DP can also "fall back" to HDMI when used with a passive (wire only) converter. I would expect that case to function at the HDMI speed. There's a lot of intelligent multiplexing that goes into modern graphics and the chip may well simply switch to a "slower" HDMI mode or the signalling buffers inside the GPU may simply be slower for HDMI signals. HDMI may well have a larger peak to peak voltage than DP and have a fixed "slew rate" that is limiting the signalling speed.

With an active DP to HDMI converter you can reach the DP limit. An active converter uses it's own electronics to convert a "true" DP signal and could do so to achieve true HDMI 2.0. I've seen laptops with two HDMI outputs from a similar intel chip and one interface was HDMI 2.0 and the other was HDMI 1.4. I would bet real money that the HDMI 2.0 port had an active DP to HDMI converter.

In short with an active 4K@60 DP to HDMI adaptor then I would expect to get an HDMI signal that can output 4K60. I would expect a passive adaptor to manage 4K30, the limit of your chip.