FJ is really strong vs grounded Peach as well because Peach literally only has one threatening way of punishing you for FJing in this position which is trying to read it with FJ up air. As long as you're not A) jumping predictably and B) drifting predictably after the FJ, then the risk/reward is skewed in your favor because if she does go for the jump read and FJ up airs and is wrong you get a decent bit of time to either punish her or set up a strong position for yourself because she's in the air for so long. One example of this is say you dash at her and then when you get to the spacing where you would FJ you instead stop there to see what happens and she goes for a FJ up air in place; you have enough time to run under her and bair or up air a lot of the time unless she drifts backwards as soon as she realizes that it didn't work, in which case you should react to that and switch to taking all of the space that she's giving up. Another example is you can run up to the same spot and FJ anyway, but drift backwards so that you don't go over her; in this case, if she goes for a FJ up air assuming you'd go over her, you can react to that and FF and take advantage of her long air time.

Another reason that FJ is so strong vs grounded Peach is because all of Peach's ground options are sorta linear; her biggest option is her dash attack, which is really easy to jump over if you pay attention to the spacing and you can punish it by either FJing past her and bairing her, or by FJing over the dash attack and then drifting so that you're on top of her as she whiffs it and you punish it with dair. This plays into what I said about not drifting predictably because if you don't mix it up well, she can use the strength of her dash attack on the ground to get you to jump and if you're not dealing with this in a varied manner then it becomes a lot easier for her to land up airs which can very likely lead to a last stock. She can also Dsmash on the ground, but this is super easy to avoid by FJing. Also I'd like to mention that, similar to how the strength of Peach's dash attack makes her up air more viable option, so too does the strength of your ground game make FJing a more viable option. If you do a good job of playing on the ground then Peach will have more reasons to try to use her Dsmash and dash attack since both of these options are amazing for beating out ground/SH approaches. What this means is that, while FJing over Peach is inherently good, you can get a lot more out of it if you manage to threaten her on the ground as well. The big reason for this is that by FJing without having a strong ground presence, you open yourself up to stalemating by letting her run under your FJ without committing. While this isn't inherently bad, it is a situation that Peach sorta prefers, because nothing happening when you decided to FJ is better than what typically happens. She also gets a slight advantage since running under you means that she's now closer to center stage so I guess it's not really fair to call it a stalemate, but typically the advantage is so small unless you jumped in a really bad situation that essentially nothing happens other than you guys switching sides. Having said that, recognizing situations where you're about to stalemate is important, because in these situations it's also usually possible to go for some kind of mixup instead of going for the stalemate, but I don't think going for the mixup is worth it unless you've established the fact that you're willing to go for the stalemate. In other words, stalemating becomes can become part of the mixup.