I have integrated a TUO Smart Button directly into Home Assistant as a Matter device with the HA app and scanning the Matter code. Now I am facing the problem described above.
Then I added another TUO Smart Button to Apple HomeKit via Matter and I then see the three states to choose from (short, double and long press) available in HomeKit.
Then I integrated the TUO Smart Button integrated before in Home Assistant into Apple HomeKit using the Matter pairing code. All three events are also available to me for this device in HomeKit.
So, there is definitely an error in the Home Assistant Matter integration, which should be fixed soon. Small manufacturers like TUO rely on Matter and can quickly go out of business due to such problems.