Can vouch for Gravity Rush Remastered, probably my second favorite game on the PS4.

I wouldn't exactly call Undertale a hidden gem, tho.

Salt and Sanctuary (Dark Souls SNES edition)
Crypt of Necrodancer
Axiom Verge

Absolutely Yakuza 0

I've been away from the Yakuza franchise since 4 ( I don't regard the god awful zombie spin-off canon... bleh). I've been playing Yakuza 0 for a little less than a month now and I feel like it's a gradual experience of several different genre of games in one. I started it off as a beat em up, a few days later I was configuring pocket cars and competitively racing in a side mission (Fuck you Fighter racer). Then I was hunting down Mr. Shakedown and exploring him for quick cash by deliberately losing my billions of yen to him only to get my money back with items that doubled the amount I lost. A week later I'm learning Mahjong, a game I adore now, then I wasted a day gambling with Majima...

My point is this game feels like multiple genres in one. I'm doing real state at the moment ffs, and I'm enjoying it.
The completion list really gives you an incentive to explore all the many different min-games and side quest because you are rewarded with points that help you upgrade pretty much every in-game ability you can think of.

I will say that I cannot stand the perverted phone sex missions. Absolutely cringy. Especially when you have the girls doing those repetitive sex poses on screen for the duration of the mini game. Maybe it's the older jaded person in me but I'm starting to lean towards the belief that Japanese people are actually as creepily weird as the stereotypes portray them. I'm put in awkward positions with my significant other when she sees that shit.

Lethal League (also available on Steam and Xbox One), may be the best arena fighting ball game ever (lol). It's extremely competitive, even within its ridiculously low userbase, and is always a blast in 3-4 players LAN. Highly recommended for good old arcade 2 buttons competitive game fans.

I'm always on the hunt for lesser known great games. Thanks for the list. I'm gonna save it to my clipboard.

Dust: an elysian tail, it has an 85 on metacritic and practically no one has heard of it. Also one of the few games where you play as an anthropomorphic rabbit.

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I really have to get round to getting both that and Matterfall. As for a pick, I actually haven't played a large number of PS4 games, but Styx: Master Of Shadows grew on me. I liked it, and don't think many people played it. Bought Styx 2 for $15 at Wal- Mart last weekend.

Gravity Rush Remastered is a good one as well.

Transistor is a great one too.  One of my favorite games from this gen.

Yeah, I highly recommend getting on that.  

I haven't played Matterfall, but most seemed disappointed with it.  Especially following Nex Machina.

The Talos Principle and Heart & Slash would be my picks.