The image noise on my camera monitor increases after I press the shutter button halfway

Noise becomes more noticeable when you press the shutter button halfway down while using a narrow aperture in the A mode with [Anti-flicker Shoot.] set to On.

[1] Before pressing the shutter button halfway down
[2] When pressing the shutter button halfway down

This phenomenon occurs because the frame rate of the live view becomes faster in order to detect flicker. The shutter speed of the live view also becomes faster in accordance with the frame rate, and the amount of light decreases. The noise increases to compensate for the lack of luminance.

This noise does not affect the actual recorded image. However, if you are distracted by it, turn off  [Anti-flicker Shoot.].