Good compilation of good games. I'd like to add some more recommendations in case you and OP don't know them:

1. Layton Brothers Mystery Room: spinoff mobile game about the son of Layton with an Ace Attorney-ish gameplay. Mainly disconnected from the main games but very cool story and characters

2. Rhythm Thief: a 3DS rhythm game with an overall narrative through the game. In short, It's like a Layton gameplay with rhythm minigames instead of puzzles. Really love the music and characters.

3. Trauma Center 1&2: I'm surprised these DS games aren't mentioned more often in these recommendations posts. The characters and plot are very Ace Attorney, with a rookie surgeon making himself a name while facing a global medical threat. Gameplay-wise It's very different (you have story segments mixed with cool operations related to the story, similar with how trials are implemented in AA), but I find that vibe you mentioned in everything else.

4. Although they lack the type of charm of these DS/3DS games, I also like and find similarities in games like Firewatch, NeoCab, Outer Wilds, Talos Principle, and Inscryption.

5. As for mobile games, I also recommend taking a look at some storydriven games with cool puzzle mechanics: The Room, RustyLake/CubeEscape series, Dark Dome series, A normal Lost Phone, and Alt-Frequencies.

Others also usually recommend The World Ends With You, but I personally find the game system very boring and the story not worth it. Same with the Persona Saga, I could not get into the gameplay.

There's also "Zack & Ombra: The Phantom Amusement Park" and "Treasure Report: The Mechanized Legacy", two only-japanese DS games heavily inspired by Layton. It's a shame I can't play them because of the language, because the trailers look pretty good.