just got up and on starting the engine and engaging the reverse gear, the handbrake refused to get lowered. What should be the way forward?
How old is your Mazda3? Is it located where the humidity is high or is exposed to moisture possibly leading to rust which could be the problem?
Generally these kind of problems are solved by someone just checking one thing and then another until they find the problem. An experienced mechanic is likely to find the problem much faster than anyone less experienced.
Who drove the car last? If the brake was applied with more pressure than you can exert you won’t be able to release it easily. You must first lift the brake handle higher than its resting position to allow the pawl to release when the thumb button is pressed.