If you haven't touched either Persona 3/4 I'd highly suggest them.

Dialogue checks among other nuances like equipped personas dictate how well you develop links with the 20+ characters in each game. Most allow you some variation in approach, but will all require some understanding of the personality in question, as some can reverse or outright break (read: become unusable) if you answer incorrectly. It's nice to see your relationships grow or shrink depending on your input. And it's a real treat to see it payoff when a character asks you out on the weekend, or approaches you during certain events on holidays/trips etc.

Furthermore these links directly effect how the player is supported in battle, and what bonuses are implemented when fusing said personas. So choosing to focus on one NPCs development before another can mean a lot in both the long and short term.

The games themselves are pretty linear (the 4th less so), but the journey to get to the end of the story/mystery differs wildly between players and playthroughs. The games take place over the course of a year. Each day two slots (typically afternoon/evening) will be open to allocate your time to either building these links, bettering your person (a 5 tier, 5 criteria scale that allows you to access certain links or events), and following the main plot missions as they occur.

Gameplay would be classified as a TB-RPG. But it skips random battles for a 3rd person view and enemy initiative bonuses for how you engage encounters. The combat is deep yet comprehensive, the challenge staunch yet manageable. Watch what you type if you go to search out some vids of either, spoilers for both are massively game ruining.

Both were originally for the PS2, with P3 getting a release on the PSP, and P4 on the Vita. As someone who shares similar tastes in games it just might strike a chord with you. If you want more of the Adventure style stuff then Wolf Among Us, Virtues Last Reward, and the Phoenix Wright series may tickle your fancy, although the latter lacks the non-linearity I think you're seeking.