I've seen a video of range test of the Air against advertised, which was verified by the person lifting off and going full speed forward until all communication lost, then setting the controller down and waiting for the drone to return on its own as programmed to do. It worked at full advertised range.
I have a Mavic Air so I follow the hobby. The mini is a good starter and get the fly more package as it has nice accessories. I had to look the specifications up and depending on frequency it is using about 1.2 miles no obstruction or interference. It will be out of sight long before that and requirements are to have visual line of sight to the craft. I don’t believe DJI is overstating the range, but I’m betting the testing area is pristine for the no obstruction/interference. Really what range helps with is keeping good control of drone within your line of sight with the environment we typically have to work with.
Mike
Of course, we don't fly that way. Fast forward uses the least power, as the tests are done, but any hovering and observing as I would do lessens battery reserve to the point max battery range getting there and back would probably be less than the max communication range. So for me, and having it kept in sight, range in miles is of little concern.