The more I test the more cars I find have been affected by this pit bug. I just did a run with the Cizeta V16T and the Ferrari F40 and surely enough both cars feel more stable after the pit stop.
I tested this in a private online lobby on Brands Hatch Grand Prix circuit with all aids off except ABS which is on 1. Both cars were completely stock with the V16T having 544 PP and the F40 had 536 PP both on Racing Soft's.
I did another test since I have a tuned F40 at 550 PP with weight ballast towards the front. It has 45/55 where as the stock one has 40/60, and the V16T has 41/59.
V16T before pit 1:33.790, after pit 1:31.252 with noticeable change in handling.
F40 before pit 1:30.646, after pit 1:29.245 again with noticeable handling.
Tuned F40 before pit 1:28.310, after pit 1:27.254 with a more stable feel again after the pit stop.
*EDIT*
Just wanted to add another car I just tested which is the RUF BTR.
Tuned at 500PP 1:33.060 and 1:31.204 after pit
Stock at 502PP 1:35.252 and 1:33.083 again both times car felt more stable on second tyres.
The tuned car has ballast towards the front and has upgraded everything and dont feel the backend as much as the stock. This pit bug is much more obvious with the stock BTR on RS tyres.
Also this bug may affect cars handling with other tyres also, it's just obvious with the RS because the tyre compound is more unforgiving.
3h ~50 laps in Brands Hatch GP with the R8 LMS ultra Phoenix ... (No aids)
Offline, "S" 15 lap race.
R8 is slower after stop and eats rear tires. (1:25,6 2nd lap, 1:26,3 14th lap, RH tires)
First 8 dry laps = same rear wear as 5wet+2dry laps after stop
(5 wet took only one bar off)
Online: (all settings to real)
Was surprised how different online feels ! (First time with a race car)
Car balance/handling is the same as offline but it feels more sharp, i have to be more sensitive with control inputs
RH:
Did ~12laps, best was a 1:25,6 most high 26/low 27 after stop only managed one 1:27,2
Interesting was that after stop i had to be more carefuel with brakes because sometimes rear started to lock before the front, almost crashed 3 times. This never happened before with my setting (bias 5/4) sign of less rear grip after stop ?
RS:
Took some laps to get used to them, lots of grip but less forgiving than RH, had to drive more clean and careful.
Best after ~10 laps 1:24,2 (room for more) after stop 1:25,x
Before stop front/rear wear equal, after stop double rear wear.
For all races:
Cars is less edgy after stop, it has more understeer and rear is more planted under braking and acceleration.
But it is not a big difference, i like it more before the stop as i can use the loose rear to get it turning and keep it tight on exit.
Before stop i had some moments under braking or out of corners, after stop i ran wide a few times out of corners.
I think i never crashed it before the stop but two times in a 2nd lap after stop (and had to crawl back to pits to repair it)
I find this very interesting because it is the opposite of what happens an 2 other MR race cars i tested.
They both are tame (understeer) before the the stop and get more edgy (oversteer) after it.
On both it feels like there is less rear grip after stop.
But true for all is that rear tire wear and laptimes increase after the stop.