How to switch off the sound of keyboad clicks?

Settings > Sounds > Keyboard Clicks is the control.

Check for and apply any updates, with iPadOS 14.7.1 being current.

If that selection is not taking, restart the iPad, switch the keyclick button back on, restart the iPad again, and then set the keyclick control off. (I’ve seen a very few and very weird weird cases with what seemed the caching of stale settings, and the toggling with a restart has cleared those.)

If using an Apple keyboard case or third party case, you may have to check those settings to turn off keyboard clicks.

For Apple based keyboard cases, such settings maybe found under the Accessibility Settings in the Settings app under keyboard settings or some other applicable accessibility setting.