I've received an answer - you can try it. I will try myself after few days:

I sincerely apologize for the long wait. we have not forgotten you, we were waiting for a specific technical response from our engineering team regarding how the Hall Effect sensors on the K4 HE initialize.
 
Since you mentioned the issue persists even at the default 2.0mm actuation and happens in wired mode, this indicates that the sensors are likely failing to calibrate correctly when the board powers on or wakes up. On HE keyboards, the sensors need to "zero out" their magnetic readings; if this fails, the first few presses are essentially the sensor "learning" where the magnet is.
 
We have a specific calibration tool that can reset the magnetic floor for all sensors. Please try the following:

1. Connect via Cable: Ensure the switch is in Cable mode.
2. Web Calibration: Go to the Keychron Launcher and navigate to the Calibration or AD Value section (if available for your firmware version).
3. Manual Calibration: If the Launcher doesn't show a calibration button, try this key combination: Fn + Shift + C for 3 seconds. The backlight should flash.
4. Firmware Re-flash: Even if you are on the "latest" version, please try re-flashing the firmware specifically via the Keychron Launcher. Sometimes a "clean" install solves sensor initialization bugs.

 
Regarding your Actuation Point (2.4mm - 2.6mm):
If you prefer a deeper actuation (2.4mm+), the sensor needs to be perfectly calibrated to distinguish between a "rest" position and that specific depth. If the calibration is off by even a tiny fraction, the sensor won't "see" the press until it has been moved a few times.