Grow beyond doesn't necessairely mean they are literally better, it means in this context that they continue where the mentors stop (passing the baton remember), but also that they will do it their own way.
Do you mean she's following in his footsteps? Then yes. But I wouldn't use the terminology "growing beyond her mentor" as a way to describe it.
What? You do realize that in a most good stories characters don't start and end the same, but evolve, right? When Poe has his Finn and Rose plan he is still handling from his flaws, making mistakes. His mutiny: same.
Through those mistakes he learned and grew, leading to the decision to pull back on Crait (something the Poe from the beginning of the film would never do. He literally does the opposite in the opening sequence). That's the point he is ready to take over from Leia. That's why she can say 'follow him' soon after.
What did he learn that puts him at Leia's level? After his (arguably successful) combat piloting during the first space battle, he gets reprimanded and demoted by Leia, then allowed to jump back in an X-Wing literally 2 minutes afterwards. So no consequences there. Then his mentor is replaced by Holdo, who treats him like a child even after his history of contributions to the Rebellion. She does withhold information from him, but does so in such a condescending manner that I don't know how he could learn anything from her. Then he mutinies and gets no reprimand from either Holdo or Leia. So no consequences there.
If you're saying he learns when to run instead of when to engage, well, does he? In the first space battle, it's entirely likely that destroying that Dreadnought (a "fleet killer" as he calls it), despite the deaths they sustained, saved the Rebellion from complete obliteration by the ships powerful guns. Then for the entire 2nd act, I don't really see anything that calls out running vs. engaging as a theme. It's not like Poe is continuously asking Holdo to let him go blow something up (which actually could have served to highlight his growth), he's simply asking for a plan, whatever the plan may be.
So if the movie wanted me to see his growth from the first space battle to the end of the one on Crait, it failed. The 2 situations are just too different. In the first space battle, they have proper ships and the odds are bad but not impossible, especially with Poe's skills. On Crait, they're flying rust buckets and there's a charged-up mini-death Star staring down at them. The cards are so stacked against them its ridiculous. So when Poe decides to retreat, I didn't think "he's learning," I just thought "This is combat-savvy Poe making a smart judgement call."
If I wanted to highlight his growth in the 3rd act, I would have had him fail during the first space battle. Let's say he gets people killed AND doesn't even blow up a single ship. So now he has this failure looming over his head during the rest of the movie, and he knows he needs to do things differently. So at the end when he sees his squad getting picked off, his retreat actually has resonance.
