Shin wise, I'd like the following:
All the improvements Kiwami 2 brought to the engine to stay. And definitely keep the ability to store weapons you pick up in fights in your inventory (this was included originally in Yakuza 2 as well but removed for later games for some bizarre reason).
A bigger Kamurocho to explore. Bring back the underground mall and make Kamurocho Hills fully explorable this time at least.
Continue to improve the Sega arcade with games not included in the series before - stuff like Super Monkey Ball, Daytona (or Sega Rally), SCUD Racer, Sega Sonic the Hedgehog (if they can somehow figure out how to get the Sonic controls to work properly on a pad) etc.
Sticking on games - I'd love to have the ability to buy a console (Mega Drive for example) in Shin and then purchase games or get them by doing side stories etc. Hokuto Ga Gotoku kinda did it this way and I loved that method. Shenmue also sorta did something like that with the home console Hang On and Space Harrier prizes.
Combat wise keep some prior heat moves as opposed to coming up with all new ones. I want quantity over quality in this regard. More heat moves = more fun for me.
Again from Hokuto, but I'd love for juggle/wall bounce combos to stay. I think HGG has the best combat of the series, I'd love for Shin to take a few cues from it.
Story wise definitely feature old Tojo Clan/support characters if the story details from last year are accurate. Plus it'd be cool to see Ichiban interact with Seijima, Majima etc.
Mini game wise bring back Bowling and Pool for sure. Tweak the UFO Catcher to make it slightly less punishing, bring back a full golf course (always loved that in 3, 4 and DS), bring Hostess Clubs back to how they worked in Yakuza 5 (my favourite way). Don't have hostess management, its been done several times now and as much as I love it, I don't want it in every game (but if they do, do it like HGG so we get tons of missions with more variety compared to how 0 and Kiwami 2 did it). Bring back spear fishing, or some kind of mini game that acts as a lightgun game, so much fun!
Bring back mission mode for Shogi, I missed it in Kiwami 2. Bring back the Mahjong League for Mahjong (its a nice way to spend a few hours!), bring back modding maybe? I hate the grind, but love the exotic gear you can get.
Also, have more side stories tied to mini games. Stuff like Pocket Circuit racer is such as cool plot across several Yakuza games.
Speaking of side stories. Do around 70-100 that older games had (skip the voice acting if need be) but keep them like newer games where they tell stories, as opposed to Kiwami where most of them were pretty straight forward. Bring Akimoto back, if Ichibans personality is that different to Kiryu's it should make for some entertaining dialogue.
Tweaks I'd like to see in difficulty - make enemies more aggressive - or at least make it super easy to get an item to do that. Up the difficulty on Hard mode so its... hard and decrease the damage heat moves deal out (its way too high at the moment). Basically make Hard mode actually hard this time! Again, HGG seemed to be on the right path on this.
Oh. And let me smack some sense into Dojima, he's had it coming for a few sequels now.