As the doctor has said, anything below 0.2 is considered by NICE to indicate success but really you are hoping for anything below 0.1 - some labs give the results to 2 or 3 decimal places while others just report it as <0.1
You won’t know that you are cancer free until a) you have had a good pathology report from the surgeon and b) your PSA has remained <0.1 for 5 years ... if you get to 10 years without the PSA becoming detectable you will be considered to be in full remission.
Usually, the first PSA test is done before the appointment to get the pathology report so it is unfortunate that yours has been done the other way round. But your report was good so hopefully your PSA will be below 0.2