I really feel like Disco Elysium treads the line between RPG and old school Adventure Game.
If you want story, its got it in spades.

The Longest Journey. It’s my favorite point and click of all time. Epic, beautiful, and fun. A couple of Babel fish-level puzzles, but otherwise a steady and engaging story with a very likable lead. The much-delayed sequel, Dreamfall, tried some things and mostly failed, but was still a pretty interesting story extension. I haven’t played the last episodic entry, Dreamfall chapters, because I’m slowly working my way through the first two again first.

It's really stretching the adventure game definition but if you are open to first person games without combat with great stories I would recommend :

• "the outer wilds" : really nice puzzles, good story, wonderful setting, definitely not linear.
• "SOMA" : a little dark, engaging story, this was an amazing experience.

Have you tried the titles from Amanita Design? They've made quite a few old-school point-and-click games, with hand-drawn graphics and cute stories despite the characters never talking.

My favourite is Machinarium.

had a good couple short playthroughs of Firewatch

Sorry if either of these already got mentioned:

• Call of the Sea
• Quern (this one is light on story, but it's a solid Myst-like game)

I like Indiana Jones and the Fate of Atlantis

Basically the entire Wadjet Eye catalogue, and the first two games in the Broken Sword series (then stop - the 3D ones are crap)

So, I’m playing adventure games (and similar games that work in the setting) with friends most Fridays. We’ve been doing this for years and have quite the list by now.

I’ll list some favorites of mine from that list. But let me know if you’re also interested in some more niche/janky games (not everything we played was good, some of it was so bad it was already entertaining again, especially when enjoyed in a group).

• Heaven's Vault
• The Case of the Golden Idol
• The Life and Suffering of Sir Brante
• Chants of Sennaar
• Pentiment
• Edna & Harvey: The Breakout
• West of Loathing

Hollowknight if you like metroidvanias. Id definitely consider it an adventure due to the exploring aspect. Up to your discretion though.

Story is fantastic imo and the visuals are stunning. Its pretty combat heavy if you're into that.

Syberia!

There's a beauty and peacefulness to it that's hard to describe. The music will stick with you, too.

Outer Wilds felt like an adventure game to me.

It's not really an adventure in the classical genre definition, but maybe Return of the Obra Dinn is something for you if you like solving puzzles and fancy murder mysteries.

You'd probably find Pentiment interesting.

Also, maybe the Ace Attorney games.

And also seconding Disco Elysium; it has some of the best writing I've seen in a game.

Another vote for Disco Elysium. For an old-school classic dripping in atmosphere, check out the 1997 Blade Runner PC game.

If you have access to a PS4 or Nintendo Switch: 13 Sentinels: Aegis Rim

A crazy and interesting sci-fi game, mixes point-and-click adventure with tower defense action stages. Story is amazing and I absolutely love Vanillaware's 2D art.

To the Moon has a great story that I still think about to this day. Not much game there, just a few easy puzzles sprinkled in the narrative. But worth it for the story and how it is told.

Gabriel Knight 3. I dont know if you have played it, but for me it is the king of adventures.

I enjoyed both Primordia and Technobabylon.

Immortals fenyx rising was a good adventure game. Good story, good writing, breathe of the wild knockoff gameplay. I really enjoyed the characters.

Deponia series from Daedalic Entertainment. The first two games are really great. The other two not so much, though.

I really enjoyed Gemini Rue and Primordia, most of wadjet eye's catalog is pretty high quality.

I also would recommend Lost Horizen, which was very Indiana Jones like, and done quite well. Another game, Heart of China by dynamix is in the same vein.

An interesting older one is Dreamweb, which has great visuals and a kickass soundtrack, but you may need a walkthrough handy since you can pick up almost any object that isn't nailed down, but only a few of them are useful.

Lastly, the old 1997 Bladerunner punches above its weight, with some amazing mechanics that I haven't seen in any other game. NPC's will notice how you treat others, and have the ability to warn other NPC's they interact with, which will influence how they respond to your questions, to the point that they will lie to you. It's also replayable, since the replicants are different characters every playthrough. The main designer did a really fantastic interview about the game on Ars Technica that I'd recommend watching (though it does contain spoilers, so beware).

It’s slow but, The Invincible was pretty good.

The Frog Detective series is pleasant, light, and overall delightful. Feels like a slightly more grownup Humongous Games kinda title.

And I do have to check- Did you play the Manhunter games?
They're super overlooked for Sierra titles, (and some lists don't seem to mention them) but they're still authentic old school adventure game.
Super cheezy though.

Free Stars: The Ur-Quan Masters has an excellent story and wordbuilding, and you can talk to all kinds of weird aliens. If you don't like the ship combat, you can set up the game's AI to fight for you.

I like the Runaway series. Well its been a long long time since I played but I remember them being good.

https://en.wikipedia.org/wiki/Runaway:_A_Road_Adventure

Rain World. Fits the vague definition with some survival elements. But it is heavy on story, atmospheric story-telling, and heavily influenced by Hinduism.

Comedy is an important part of Point & Click games for me. If anyone has other suggestions, I’d love to hear them.

This list is in order of my favorites:

• Paradigm
• Darkside Detective
• Everything by Amanita Design
• Cleo: A Pirate’s Tale
• Feria d’Arles
• There Is No Game: Wrong Dimension
• Lost In Play
• Thimbleweed Park
• Bertram Fiddle
• Will of Arthur Flabbington

this will be a little hard to find but Morpheus 1998 was great

I know many people did not, but I really enjoyed the King's Quest reboot.

A while ago I played through the first two Broken Sword games, and I enjoyed them very much!

An Point and Click series I really enjoyed: Deponia. It's focuses more on humor, but also has great writing.

It's a big stretch on the definition, but try the Hitman Trilogy. There are tons and tons of solutions to achieve the kills without trying for tricksy, difficult stealth challenges - just by recalling a bunch of hints you've seen/heard by wandering around the region, and combining them in fun ways.

Basically, if you see that the target is inside a complex guarded by two armed men, you shouldn't be trying to flick a coin to see if you can turn a guard just long enough to use your garrot on one, and hide him around a corner, all in 10 seconds. You SHOULD, instead, look for options like:

• Find a pizza delivery guy, get him alone, knock him out, take his uniform and pizza, and greet the guards so they let you in
• Set off an alarm in a nearby room that causes a guard to go shut it off
• Call the target on the phone and tell him you want to meet about his secrets. Then, he leaves the complex himself with one bodyguard to your proposed meeting spot "right underneath the suspended ornamental anchor".

What's often misleading about the games is they orient themselves around all this equipment you can bring in, but the best way to explore a lot of levels is with no equipment at all (sometimes not even a pistol). Granted, the game changes in speedruns and other challenges, but it DOES feel like playing a Monkey Island game at times.

Oh! Can’t believe I forgot, but you should also play Under a Killing Moon, and then when you’re done and completely in love with it, move on to The Pandora Directive, Tex Murphy: Overseer, and Tesla Effect. They’re a series of hilarious retro-sci-fi gumshoe detective comedy puzzle adventures. It’s like Maltese Falcon, Blade Runner, the X-Files, and Young Frankenstein got put in a blender. They’re amazing.

Have you tried Resonance? It's a mystery adventure game set in modern times where you play as four different characters whose stories interconnect. It's been a while since I played it (a decade or so?) but I remember that it had an interesting game mechanic that let you use memories like items in various interactions, as well as a number of puzzles that I rather liked the design of.

Legend Entertainment produced some great adventure games throughout the '90s. The wiki article has a list of them, and several are available from GOG.

NORCO is the best old-school point and click adventure I played recently. Great pixel art. Great writing.