What "CD display" are you referring to. I am not aware of any display, and in fact asked my dealer over a year ago if there was a display I hadn't yet discovered. At least on my '18 model there is no display to indicate when the CD kicks in.
The following comments apply to a US 2020 2.5L gasoline normally aspirated. The experience of others may vary.
Real time cylinder deactivation can displayed on the touch screen at Applications > Fuel Economy Monitor. You will not find this anywhere in the 714 pages of the PDF owners manual.
If you want to use the touch screen for something else, a handy alternative would be to set the right instrument pod to the "Info" setting that shows real time mpgs. For example, in a recent test in normal (not sport) mode, I found that after accelerating to 50 mph and then easying off the throttle or holding it steady, the real time mpg monitor might jump up to 45-55 mpgs and the cylinder deactivation display shows two cylinders running. Then, taking my foot all the way off the gas pedel, the real time mpg needle buries at 80 and zero cylinders are shown to be active on the touch screen. At low speed, around 15 mph, I've found two cylinder mode tops out in the the low 40's mpg range; all the way off the gas again buries at 80. I never use sport mode so others may or may not see differences.
The long and short is if you use the real time mpg monitor, any jump into the 40s or above would tell you cylinders are shutting down; buried at 80 tells you all 4 are shut down.
I find the cylinder deactivation/reactivation in this model to be entirely transparent with no noticeable change in engine noise, vibration, nothin'.
I think you're confusing engine auto stop/start (engine cuts off when you pull to a stop, then starts again when you take your foot off the brake) with cylinder deactivation. CD on GM and Mazda vehicles is pretty much unnoticeable (I have worked for both brands). Auto stop/start though is very noticeable on GM vehicles
At full stop idle in drive the cylinder deactivation display in the above referenced year and model shows all 4 cylinders running without exception in my brief tests. That's different from other makes that tout cylinder deactivation or shut down/restart at idle. That's a good thing. Constant reignitions from full stop idle can't be anything but additional wear and tear on the motor and starter.
In fact, I've found all 4 cylinders running under all conditions up to 10 mph which suggests Mazda wants to be primed for get up and go without any lag or unusual noise or whatnot, keeping the process transparent.
Some confusions may arise from Mazda's use of the term "Stop and Go" for something entirely different.