many folk run better indoors for a number of reasons so the difference between your indoor pr and your outdoor pr is not exceptional and does not say anything in particular about you as a runner.
however, that session you detail where you run 3 x 800m repeats at your 800m race pace is revealing.
your four in-season races average 2:37.5, your 3 repeats average 2:39. you don't mention the recovery but unless your recovery was something silly like 20 minutes this says you are strong enough to run a lot faster than 2:32 and we need to consider the reasons why you are not yet doing that.
1. basic speed - what is your pr over some shorter distance, like, say 200m or 400m. if you can run 400m under 70s then you should be able to crack 2:30 for 800m fairly easily. if you cannot yet break 75 for 400m then maybe you need to work on that a bit to see an improvement in your 800m pr.
2. pacing - what are you running the first lap of your 800m in? do you go out too fast and then die in the 2nd lap, or do you start too slow out of an excess of caution and find you are speeding up towards the end, or are you a very even-paced type of runner with two equal laps? it also makes a difference if you are racing or time-trialing. if you are winning easily with no one to push you it is difficult to make real progress. on the other hand if you are essentially ignoring the other runners and just trying to pace yourself then it is easy to miss the benefits of racing.
3. doubling - are you running other races in meets before your 800m? in my experience a lot of HS athletes get too many races in meets and this limits their ability to make real progress. its good for their teams, but not so good for them as individuals.
cheers.