My PS4 Controller R2 Keeps Pressing By Itself, The Car Accelerates On Its Own

Your two observations together, a resting value of 0.12 and a trigger that feels loose and does not spring fully back, point strongly at the return spring.

The DualShock 4's L2 and R2 are analog triggers. Each one moves a small sensor as you pull, and a little coil spring pushes the trigger back to rest. When that spring breaks, pops off its post or loses tension, the trigger stops returning all the way. The sensor then sits slightly pulled, and the game reads a constant partial press: slow acceleration in driving games, random shots in shooters with a low fire threshold.

Less often, the sensor itself is worn or dirty and gives a non-zero reading even when the trigger is physically at rest. You can tell the two apart in the test. Push R2 fully back to its rest position with a fingertip and hold it there. If the reading drops to 0.00 while you hold it, the sensor is fine and the spring is the problem. If it stays at 0.12 with the trigger pressed fully home, the sensor is the issue.

The spring repair is a well known job: open the shell, refit or replace the spring, close it up. Replacement springs are inexpensive and often sold in packs. If you would rather not open it yourself, a repair shop will do it quickly, and out of warranty it costs far less than a new controller.