So, I just completed a run of the game where I did everything in the reverse order. I know what you're thinking : "There's no order in BoTW !" Well, you're not wrong – I mean if there was one set in stone, I couldn't have done this run in the first place -, but clearly the devs intended you to do some things before others, and we know some dialogue changes depending on whether you have the MS or not, so I tried to see as much as this alternative dialogue. I started by getting the MS, then did Gerudo > Goron > Zora > Rito, then went to Impa and got the memories. In reverse order, for good measure.
So here's a list of things I found out, in no particular order :
-If you reach a divine beast before going to Impa, Zelda will cut the middleman and brief you herself about the divine beasts
-When you reach Riju with the MS, she just won't mention it. I was kinda disappointed as when you don't have it, she brings it up as something the Hylian Champion should have, so I figured she would recognize me as such if I met her with it, right ? Nope.
-If you refuse to take the dating class, Link will still look away in embarassement when the teacher ponders if his heart is taken. At this point he only met one NPC, so clearly this means that Link actually loves Rhoam.
-The Rito elder, when seeing you have the MS already, ponders if you're Link.
-While Link's reaction doesn't change in the Gerudo dating class, when asked by Teba why Link wanted to calm Medoh, I couldn't pick "to save Zelda"
-Bludo will say that Link has good stuff when he notices he has the MS
-Dorefah never expected Link to not have the MS, so he just says that given that Link has it he probably won't use the lightscale trident much, but he can still have it.
-If you go to the Hateno lab before going to Impa, you can't light the furnace and Purah's assistant will mention they need Impa's autorisation (really ?)
-When going to Impa, she notices you already completed the Divine Beasts, but she's too absorbed with the slate's missing album to tell you to go to Ganon and to notice you have the MS. She will only comment about the MS and send you to Hyrule Castle after you restore the slate's functionalities. Talking to her again before that will just have her tell you to go see Purah.
-If you have not activated any towers besides the one on the Great Plateau, you will get the sheikah detector when Purah restores the slate's functionalities. Which makes sense.
-Sadly I forgot to check it the first time I went to Impa, but after I found all the memories Paya's diary was fully written. A clear contradiction, as I only spoke to her once, yet the diary contradicts that. Also I thought the last page was tied to the Kakariko shrine quest with her, but it seems it's not. Maybe it's tied to the number of divine beasts completed ? I dunno.
-Find the Fairy Fountain, despite being a main quest, DOESN'T need to be completed to get the true ending. I was surprised by that, actually. That said, good luck getting all memories without it ! So it's not really a big deal.
And that's about it. I don't think I missed anything (except Purah's alternate dialogue when lighting the blue flame before speaking to her, but this is well known), so in the end there's not much different dialogue,but tbh I just needed an excuse to play through the game again.
If you have anything else, feel free to add !