There should be no guesswork involved.
The "in service date" should be printed on the dealer's invoice/receipt that you got for the software updates. I see it in the second row of boxes at the top of a Mazda dealer oil change invoice/receipt. My Toyota receipts show it as well--they call it "delivery date". This is evidently industry SOP. Barring that, if you got a CarFax the original titling date should be shown there.
The "in service date" is the date the original owner bought the vehicle. The manufacture date on the door label has nothing to do with warranty terms. Your CPO limited warranty clocks to 4 years / 48,000 from that in service date,
whichever comes first, if that needs to be said. The exception is if the original 3 / 36,000 had already expired when you bought it. In that case you get 12 / 12000 miles from your purchase date as
@Tchman2016 illustrated.
By the way, any service performed in or out of warranty is guaranteed for 12 / 12,000, another common industry practice. So, for example, if you had a service done 6 months before the warranty expired it is covered for 6 months past warranty expiration, assuming you don't exceed 12,000 miles in the interim. If you paid out-of-pocket, then it is 12 / 12,000 from the date of service regardless of manufacturer warranty terms.
I don't know what all you had on your laundry list of problems, but as far as the shifting issue is concerned (been there, done that under warranty per a TSB) I can see where you might have had a problem. I wasn't in the room, but If you asked them to throw the software cannon at it, updating all the modules, that's not how troubleshooting is done, right? You present the specific problem with whatever support you can provide and take it from there. Depending on what else is on your laundry list and the attitude going in responsiveness might vary.
Taking the focused approach, if you went in with the following TSB, to take one example that has been discussed in several other threads, or any other like TSB that fits the situation, I would expect a free diagnosis and update of the software if the limited warranty is in force and if the problem can be recreated. "Verify customer concern" is another one of those SOPs as the first troubleshooting step. The following TSB, for example, states it is covered under the limited warranty, not the drive train warranty.
file:///C:/Users/jdelf/Documents/Auto/2020%20Mazda%20CX-5%20Touring%20Reference/MC-10185048-0001.pdf
If all else fails, I would ask for a tech to join me for a ride to recreate it and if you can't recreate it you can be expected to be SOL.