Not sure if it will work, but give following a try -
Turn on Emergency SOS. Restart your phone. Turn off Emergency SOS and then restart your phone again. Press the power button 5 times to check the issue is resolved.
It's ndeed sad that it did not work. I am afraid, you may have to book for a repair and let Samsung have a look at the issue.
In the meantime, you could change the emergency contact number to some random number like 000 and / or increase the countdown duration.
I am not sure tbh, but if you going to factory reset your phone, before doing that, try resetting all the settings.
Settings > General management > Reset > Reset all settings and restart your phone.
Note that you will have to set up Wi-Fi and Bluetooth connections again and all your custom settings will be reset to factory default.