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You could take a look here:
/t5/Xperia-Z5-Z5-Compact-Z5-Premium/How-to-turn-off-vibrate-but-not-sound/m-p/1158228#M24812
To turn your device into silent mode, reduce the volume to 0 then press again volume button.
In order to not receive a notification from a specific app, disable vibrations from each app.