Hello. the forum is always there to help. The climate works fine. It is worse at the front. The passenger is worse than the back. It is poorly cooling the driver's area. What's the problem?
as mentioned above, it could be the blend door (controls direction of air selected on dial) as they are called may not be closing or opening fully.
Here is another kicker, on each blend door (if more than one), there are usually holes. The blend door itself is not a solid piece (of plastic). The holes in the blend door allow the door to move when the fan is on high; otherwise, the motor would have to fight the full force of the air traveling through the duct/blend chamber, thus causing more stress on all parts.
Also, the blend door will have foam or some other semi-porous material covering the holes to limit the amount of air that "leaks" past the door and directs 90%+ of the air to where you want it to go.
It is possible, that maybe the material that normally covers the holes on the blend door(s) has failed or is compromised and is allowing more cold/hot air to the back vents.
It is also possible that the main back vent duct is nearer the blend door and more air naturally goes to the back before it goes to the front. I do not have a schematic and I've never seen the Mazda blend chamber, so I cannot be for certain what is actually going on.
In the end, it could just be a design snafue and how the main front duct and main rear duct are in relation to the blend door and the rear main duct "wins" getting the coldest or hottest air first.
good luck in finding a solution.