There is aging, there is wear, and there is failure. The check for cracking and such above is for aging. These checks are all good.
Failure is where the fabric has ripped or been cut and you a blowout or a bulge.
The wear threshold is when you have a wide flat part of the rear tire, and in that flat spot you can see the tire fabric. If your tires don't have cracks or anything, you can replace a worn rear with a semi-worn front (The rear tire will wear down faster) so that you get all the tread you paid for. Then put your new tire on the front.
BTW, DO NOT "ROTATE" TIRES. That is, never just take the worn rear tire and swap it out with the front tire to equalize tread wear. Wear the back one out, put the semi-worn front on the back and put your good tire on the front. Or, replace both if you like. Remember: Always have your best tire on the front wheel.
For a bit of background on that last point (unfortunately described as tire rotation), read here:
https://www.sheldonbrown.com/tire-rotation.html