Finding Yuanda Zhu is the motivator for the story in Shenmue 2. While I didn't love that they basically reused that plot idea for Shenmue 3, it's also not a big deal if it acts as the compass to steer Ryo along the story.
Thing is, in Shenmue 2 a lot of stuff happens up to the point of meeting Yuanda Zhu. We get an introduction into so many characters and their development. S2 was mostly chapter 2 of the story, so basically the beginning. It did well to establish the main characters, setting and build everything up. Shenmue 3 failed to do this even when they set up the retread about finding Yuan to act as the line to delve deeper into the Chi You Men and lore about the mirrors. The only thing we got was some development for Shenhua.
Also, dead right that at the end of a long chase we need some sort of payoff. We got that big time with Yuanda Zhu, not so much with Yuan.
I even thought the conversation with Zhu was less than it could have been, I feel like more should have been established as to how he really knew Iwao and Zhao, but perhaps those details are unimportant (they are martial artists studying together and that was about it). Still, there's definitely payoff because I believe this is where we learn for the first time that Lan Di is Zhao's son, and you get the light show with the Phoenix Mirror.
But yeah, you are dead on with everything else. Shenmue 3 had none of the buildup Shenmue 2 had. In Shenmue 2, there was the arc with the Wude, the arc with Xuiying - bad ass character by the way, I miss her dearly - the establishment of Ren as an ally, and impressing the scout by fighting those 3 huge Street Fights was epic even if it didn't really affect the overarching plot (Rod Stunt had more character development than Broom Girl - and the scenes with Chunyan are really powerful). Being taught the Counter Elbow Assault happened naturally as part of living under Xuiying, it was super symbolic when he ended up using that move against Dou Niu - in Shenmue 3, having to learn a specific move that would magically make Ryo strong enough to beat the boss was so unnatural - and it happened TWICE.
I did like both scenes with Niao Sun quite a bit honestly but there should have been so many more - one with her and Lan Di interacting, for example. Also, a novel idea: perhaps try introducing this woman to the player by mentioning her fucking name.
The game should have gone something like this:
Bailu: cut the fluff - make this a 5 hours tutorial area, not a 15 hour slog. The same basic premise - defeating the thugs who have taken over part of the village while they look for the mirror - could have existed. Rather than finding some pointless trinket in the bell tower, you still could have battled Chai and received a revelation from Elder Yeh before heading to the next area.
Niaowu: The Red Snakes terrorizing the town should have actually been intertwined in the story. There could have been plot lines associated with the Snakes trashing the temples (maybe they were looking for the mirror or some clue that should have justified Niaowu in the first place), that brought in characters like Hsu and Broom Girl, and the Zhashou lookalike) and actually developed them. At the end of the section, Ryo should have defeated the Red Snakes and learned about the Chi You Men's hideout at the castle. Niao Sun should have been a major player in this section and actually developed as a character, the cliche disguise plotline should have actually had a point.
Castle: While ideally the entire Baisha section should have remained intact to allow some major Chi You Men development, at the very least the castle should have been focused primarily on Niao Sun and Lan Di. The Red Snakes should have been out of the picture by this point. The betrayal by Niao Sun could have had some impact if her and Lan Di appeared in the story together, sooner. This "Warring Kingdoms" idea Suzuki promised should have been realized - those comments made me really excited for Shenmue 3's endgame. We got a shell of what the Yellowhead Building offered.
Yuan could have been rescued at any point - end of Bailu, end of Niaowu (this would have been the best spot, and allow for some exposition before the final section), or during the castle raid like it actually happened. They could have justified Ryo and Shenhua's continuing pursuit of the Chi You Men in a number of ways (obviously Ryo wants revenge but they could have given Shenhua a real reason to pursue her destiny and help stop the Chi You Men).
