Not an essay time:
I have to say, the specials were rather enjoyable. I wasn't expecting to see the Magikarp Salesman, but I'm not going to complain.. I did enjoy the nods to previous series within the first episode, ie Oshawott and Piplup displaying animosity as a nod to Best Wishes and Rowlet resting on Ash's head as a nod to Sun & Moon. Seeing Saturn heading to Stark Mountain to capture Heatran I felt was a partial nod to the events of Platinum where Charon wanted to acquire Heatran inside Stark Mountain, and in that regard it's nice to see Platinum get some kind of love, in any case I do think it was smart of Saturn to lob a Dusk Ball at Heatran as that has the best chance of capturing the pokemon. As-is on brand with me, there were things I failed to notice, like Saturn's Dusk Ball melting when Heatran went berserk, nor did I count how many life plates were surrounding Arceus in the fourth episode, but when I saw a later screenshot, I saw that it had added two extra life plates to reflect the Pixie Plate and the Legend Plate as those didn't exist in Gen 4. During the third part, when Brock relays Cynthia's idea to collapse the ground, my immediate thoughts were "Ah, this would be right up Team Rocket's alley, digging a pitfall." but the idea itself in general made sense to buy some time. All in all, I felt that these specials felt like they'd have fit in to the DP series, there were proper stakes, everyone was made use of and Arceus wasn't just a silver bullet solution to the problem, it assisted when it was necessary to do so. Also it was a good way to showcase elements of Legends Arceus in a non-spoilery way. One thing that baffled me though was Team Galactic itself. Considering Mars, Jupiter and Saturn were arrested in DP152, essentially dismantling Team Galactic, I'd like to know how they were released, I'd like to imagine Officer Jenny couldn't keep them in custody forever (considering Cyrus is off world) and thus let them go after a certain period of time.
At least Goh didn't add any new 'mons to the Sakuragi Institute roster, though I felt that the writers thought it'd be best not to give him new captures as these were Amazon Prime specials.