Overall, while I'm probably not as critical on Dawn's usage in JN as some other users online (I don't actually think she needed new evolutions per se, for example), I do think she unfortunately got the short end of the stick in spite of her large amount of returns.

Specifically, I believe she was an unfortunate victim of the latter half of Gen VIII needing to promote Sinnoh and Hisui, since a lot of her return appearences feel more about spotlighting what he represents (the Gen IV player character) than her character, especially considering the Dialga and Palkia arc turned out to be fundamentally inconsequential to JN and Arceus Chronicles was a deliberate out-of-series 'reunion show'-esque adventure for the DP gang.

I actually think her first return is the relative best in this sense, as the general idea of adventuring with Chloe and passing down some of her experience with Piplup and her relationship with her mother is a good one and there were some solid interactions between the two. I do however think that her writing felt somewhat off: stuff like getting distracted on the way and climbing trees for fun was kinda weird coming from her (especially the latter, as that's much more of an Iris thing), as while she was often reckless and eccentric I don't recall her being this brand of an oddball in DP. I feel while the general idea of teaching Chloe about enjoying the journey and not just go straight to the destination isn't bad, I believe Dawn either wasn't the best character to teach it, or at least not in the way the show went with it (my own attempt at things would've probably involved something like highlighting Dawn's experienced recklessness as causing the temporary rift between her and Chloe, contrasting dangerous shortcuts to the safest option to get to Eterna City as a way to still push Chloe out of her comfort zone and relate a similar message). I do however respect how this arc ultimately feels like the one Dawn return in JN that actually tries to be meaningful and purposeful for the story in some fashion.

I'm far more mixed on the Dialga and Palkia arc: while being kinda inconsequential to JN is a mark against it, I do feel there's a lot of very fun concepts and ideas in the arc: reversing time so Pokémon devolve all the way to Eggs is incredibly nightmarish, and what little we see of most of the alternate world is pretty tantalizing (especially the idea of Dawn having been a professional trainer here, but ultra-confident Goh and hacker Chloe really steal the scenes they are in). The arc however really suffers of just not having time to develop a lot of these fun concepts, and the ending relying on a very literal deus ex machina resolves the matters very unsatisfyingly and not making it feel like the cast really did much to solve the crisis all things considered. Not one of the best showings for either Dawn or JN, in my opinion.

The Arceus special is a bit of a special case: there's a lot of very self-indulgent continuity and it's only slightly less inconsequential than the Dialga and Palkia arc (and only because Roserade does appear in Cynthia's team later), but I feel being a made-for-Amazon special outside regular episodes gives it a free pass as something outside JN's regular story. Reuniting the DP gang plus Goh makes Dawn's presence a bit more understandable here, and I think she gets at least a better showing in terms of proactivity and personality compared to the prior listed episodes. While she still doesn't come off as 'central' to the arc (I'd argue Brock gets the best portrayal in terms of showing progress of him working as a doctor there), it's an enjoyable enough adventure that gets some props for feeling like an old school villain arc in JN, and successful enough in its goal.

Her appearing in the Ash VS Leon fight honestly felt more like her and Chloe being there to fill Goh's seat after he left than actually giving much to do to either, given they mostly offer some commentary here and there and Dawn fundamentally vanishes from the story as soon as the match's aftermath is over. Part of me kinda feels like she may as well have been one of the cameos watching on TV, given the amount of importance felt roughly the same.

All in all, I understand why her appearances are pretty controversial: there's definitely little done with her compared to her amount of appearences, and I feel the biggest issue is also that the show didn't just bring her back to Sinnoh but also didn't really elaborate much on what she's up to beyond generically doing Contests, which is probably what makes her come off as stale (I assume May would've had similar issues going by her cameo during the finals implying her participation in Spectaculars and being back in Hoenn, but given she didn't get a dedicated episode, it was far less noticeable). All in all, a shame that her returns weren't handled the best all things considered, even if I was happy to see her back.