On my old freelander 2 you could switch the beeps off with a sneaky fix. I googled it and it was on some forum somewhere but basically you sit in the seat, switch the ignition on to stage 2 but don’t crank it over and then unbuckle and buckle up the seatbelt 10 times within 60 secs. This then displays the red seatbelt light on the dash and beeps once for a few seconds and low and behold, you are beep free when driving with the seatbelt off with only the red dash light lit up. This works like this until you reverse it by doing the same thing again.
Before anyone thinks I’m a lawbreaking numpty with a death wish it’s because when I had the vehicle I spent a considerable amount of time driving it off the public road with a lot of stop start driving opening gates, looking at jobs etc where the constant on/ off of the belt was a pain in the ar£e.
It also works on fords as I used the same fix on a number of our company ford focuses. My current work truck which is a ford ranger (too old for beepers thankfully) is also a Mazda underneath hence my post here, it might be that your Mazda uses the same “cheat” to turn off the beepers. When I asked at the landrover dealer where they recode things on the ecu for various reasons ( they turned off my auto door locking) they said the seatbelt buzzer couldn’t be switched off. Ha.