I'm using an LG 27UL550-W on my M1 Mac mini, and I have never had any issues on any resolution or with either type of connection.
I've tried both HDMI to HDMI (2.0) and Thunderbolt to DisplayPort (1.4), and seen no difference. Always 60Hz, no flickering, no colour change on wake up. It takes a few seconds to wake up, which I assume is normal.
Since I haven't seen any difference between using the HDMI to HDMI and Thunderbolt to DisplayPort, I've decided to use HDMI to HDMI, leaving both Thunderbolt ports free for other uses.
For those who experience washed out colours, I would recommend calibrating. I've calibrated the monitor using the advanced calibration under System Preferences>Displays>Colour Profiles by option clicking Customise. Following Apple's on-screen guideline, I set the brightness to 0, and contrast to 100, before continuing with the calibration.
I haven't touched any other settings on the monitor, as I have no idea or found any clear explanation to what they actually do, and I've left the HDR option under System Preferences>Displays off, as it seems to change the original interface colours. I have yet to find out whether the monitor shows HDR content even without that option checked. Any information/recommendation on the optimal monitor settings will be appreciated.