Just a couple of things. I wonder if this would be better in the S23 threads, since we might expect similar models with similar updates might have similar bugs, if this is a bug.
In the meantime, what keyboard are you using?
Have you tested another keyboard? If you're running the Samsung keyboard try switching to GBoard or vise versa as a comparison to see if one is quieter than the other. Switching and switching back could also correct a glitch and return function, maybe.
When you were taking steps to see if you could quiet the keyboard did you test an increase in volume to see how loud it gets or to see if the volume changed at all?
Speaking of volume changes, just to be sure, these are the steps you've taken for;
GBoard
To adjust the keystroke volume on Gboard, navigate to Gboard settings within your phone's system settings, then find the "Sound on keypress" option and adjust the volume slider. You can also disable the sound altogether by toggling the "Sound on keypress" option off.
Samsung
To adjust the keystroke volume on a Samsung keyboard, you'll need to access the keyboard settings. The specific steps depend on whether you're using the default Samsung keyboard or Gboard. Generally, you'll navigate to Settings > System > Languages & input > Virtual Keyboard > [Your Keyboard] > Preferences to find sound or vibration options for key presses.
If it is a bug or glitch from the update, have you tried clearing the Partition Cache? When you said that you cleared the cache earlier, you just said "cache" so I assume it was the keyboard cache that you cleared. To clear the partition cache, Power off the device>hold the Volume up button and the Power button until the Samsung logo appears, then release the Power button but hold the Vol button until the bootloader menu appears. Once the phone has booted, use the up and down Volume buttons to navigate and the power button to select and select Clear Partition Cache, and reboot.
Let us know what you find.