This is half true.First I don't use racing softs, too ultra grip for all cars, but when getting back to home can test that for you.
Answering already what I have noticed by earlier playing; after pit stop you have to drive one or one and half lap(depends track jadajada) easily to warm your tires slowly to keep them on stable temperature or you spoil grip because of too much skidding/sliding.
After warm-up of tires those work exactly same as 1st stint tires.
On Audi ultra driving is easier if tires are sliding a bit and that might be reason why you got better times with 2nd stint burnt tires.
It seems to helps to treat them well but there still is a difference.
I just did a 30 lap online race with stop in 15th lap.
I was very careful in first two laps after stop and then started to go faster.
Still more rear tire wear after stop and slower laptimes.
Before stop i had ~2/3 rear tires, at finish just over 50.
And as i said before car is more edgy before stop and i slide more often , after stop it is mostly understeer so i should use less rear and more front tire.
Maybe there is only a small difference in wear but this gets amplified in races with increased wear like the "S" ones ?
(2sec. Tires spin there is like 20sec. Spin online with normal wear ?)
Laptimes: (setup i posted before, RS, no aids, DS3)
Before stop:
Best 1:22,7
Usually between mid 23 to 24
After stop:
Best: 1:23,989 and that was a "freak lap" only did one more 1:24,9 rest all low 25 to 26.
(Also the fastest lap was in 29. where the car started to loose understeer again because of worn rear tires)
2 spins (out of corner) and a few big moments in first 15 laps (i got tired for a few lap, not good with this car)
1 offroad adventure because of locked rear brake, 1 big off in the gravel trap while pushing hard after the stop.