draft picks do impact prestige, but only after the draft. basically, right after the NT/PIT championship sims, you will have your new prestige - i can't remember if there's a few minutes of delay or not, but if so, its very brief, and its many days before the draft (where you get the draft boost). this is your prestige based on the performance of the season (including regular and post season). you go through coach changes and RS2 with your season-performance based prestige, and then after the draft, if you have draft picks, you will also get a prestige boost, which is temporary, it only lasts one season - less even, in 3.0, because its really only for the next RS1 (recruiting session 1).
you can see in your case, your season based prestige was a B+. this is based on your prior 4 seasons of performance, and in no way factors in the draft picks from the previous 4 seasons (or any other draft picks). this is on the history tab. the prestige at the top of your general view shows A-, which means draft picks pushed you up from a B+ to an A-. with the #2 draft pick coming from your school, that will happen decently often - the #2 draft pick is worth probably about 1/3rd of a partial grade, or perhaps a tad more. so if you had like, an 89 B+ before, now you are a 90 A-, maybe a 90.5 A-, something like that. but this only helps your very next RS1, it doesn't have any impact on your prestige 'long term', and i say 'long term' because the prestige window is only a fairly short 4 seasons in the first place.
the 'season performance' prestige, meaning the history page listed prestige, is based on 3 things - your performance the last 4 seasons (current season counts for more than the oldest), your baseline prestige (which is fixed per school, tech is either a B or B-, that is listed somewhere on these forums) - and lastly, conference prestige. i just mention this because conference prestige is often forgotten - it is just the average of your 12 conference teams' prestige. conference prestige has a pretty significant impact on your prestige, and conference prestige changes every season, so when you say the only thing different - i figured i would mention, around the margins, conference prestige does have some impact and does change every year. i often will look back at the team history to get a sense of 'what does it take for a B+ or an A-' or that sort of thing - and that works pretty well but conference prestige does disrupt that.