I really enjoy both series, but Yakuza is verrrry far from a 'poor man's Shenmue'. I think the comparisons really put people off.
Think Yakuza meets Life is Strange is the best way I have been able to put it. Lots of focus on slow deliberate character moments, exploration of a smaller area and interacting with that area to search for clues.
Just throw in the fight scenes from Yakuza and set it in the Far East and you get the vibe.
Yakuza and Shenmue fall into completely different genres, when you break both games down to their core elements.
Yaskuza is a beat 'em up RPG, it really is like a PS2 era update on older 8bit games like River City Random. It's all about fighting groups of enemies and bosses. You collect money from them like RCR, and use it to buy things. Yakuza is more streamlined and linear than Shenmue, even though the game has open-ended playing fields.
Shenmue 1 is a virtual simulator adventure game. You are basically in a virtual snow globe with a large assortment of unique NPC's. Those NPC's operate on a 133 day timescale that starts on November 29th 1986 and ends on April 15th 1987. The NPC's have simplified lives of their own. The way you interact with the NPC's will have some affect on ending of the game.
The original Shenmue games were designed to read off each others save states. Depending on what day (in the game world) you completed Shenmue 1 on, it would carry over to Shenmue 2's start date. This will then affect what events could happen on the first day of Ryo's arrival in China. Different NPC's will be located in different spots on different days. Also, the seasonal changes affect the gameplay areas as well. Which will give each person playing a slightly different experience based on what they did in the first game. Otherwise Shenmue II defaults to February 23, 1987 as the start date. But you can start Shenmue II at an earlier or later date in 1987 with your Shenmue 1 save data.
I'm not even sure if this was carried over to the HD Shenmue collection? I hadn't bought it yet. I own the original on Dreamcast and obtained the sequel through other means ( I also purchased a copy on the 360). But the save feature carry-over works for Shenmue 1 and 2 on the Dreamcast.
Outside of that, Shenmue has a fighting game element to it as well, where you can learn new fighting moves from different people in the Yokosuka area. Which will affect the way fights play out. Shenmue also encourages the players to explore every area, which adds a puzzle solving element to the game.
The only other games that come somewhat close to this are Quantic Dream titles, and most of those are set on smaller scales. Some people also say "Life is Strange" as well. But I have never played that series.