[toni-a]

Without knowing the settings, quite useless info? I can make good images (noise wise) with my 6D (and even EOS M) and awful noisy images. You have to use the right settings of course.
It appears that she underexposed a lot, as you mention "lifting shadows". So, yeah. When taking photos, do check the result when taking them, and adjust settings when things are not right.

If I remember correctly, the M3 uses a similar sensor as the EOS 80D, but it performed a bit worse.

M3 uses same sensor as 750/760D not 80D, (it doesn't have dual pixel autofocus) .
of course when you know your camera you can take better advantage of it despite limitations, it's never the cameras fault for bad pictures, but it's better nonetheless to have a good performing camera straight from the beginning
M3 sensor is better than almost any sensor produced 15 years ago, it outperforms Canon 1Ds that used to be considered state of the art camera from sensor side and at the time, when 1Ds was in production nobody complained about its dynamic range and plenty of awesome photos were taken with it.
M3 isn't bad at all, with 11 f stops dynamic range, if you have non usable pictures it's not the camera to blame, of course 14+ f stops would be better however I am sure even such a sensor will only partially solve the problem