I don't own a KYT8900D, but I did download the manual, and I went over it to see if the power button has a short-press function. If there is such a function, I wasn't able to find it in the manual.
I find the notion that the radio has a function associated with the power button, not mentioned in the manual, that clears up the reception to be very unlikely. If there were a function that improves reception for weak signals, then the manual would surely emphasize it for marketing purposes. I also find the notion of the power button having a secondary function to be unlikely, unless the radio is so crammed with functions that there is no other button to hold the function. Putting multiple functions on the power button is bad design; hold the button too long, and the radio switches off, which would annoy operators.
I'm just guessing here, but I think that there's an intermittent connection somewhere in your setup, and pressing the button fixes the intermittent connection temporarily. I suppose that it's possible that the bad connection is in your PL-259 coaxial connector, especially if you soldered it yourself and you don't have much practice soldering PL-259s, but that seems unlikely because pressing one place on the front panel would be unlikely to flex the connection between the coaxial cable and the connector.
The most likely explanation seems to me to be an intermittent connection inside the radio. The problem could be a cracked surface-mount component, a corroded connector pin, a poor solder joint, etc. Good quality control can prevent such defects from leaving the factory, but QYT seems to be a company that is new to making radios, and their reputation for quality control seems to be mostly unknown. You could try pushing on the front panel near the power button. If that improves the reception, then that would support the intermittent-connection theory.