I did this for the Witness - it really helped to think out some of the puzzles if scribbled possible solutions down. Oh and Obra Dinn to an extent - mostly things like 'I saw this guy hanging around in this memory - could he be X'?

Return of the Obra Dinn

Myst and its mainline sequels, especially Riven will generally require pen and paper for almost all puzzles (except for the godforsaken train tunnel puzzle). Cyan has also made Obduction which is very similar and I ended up using pen and paper to take notes for. Quern: Undying Thoughts is a Myst-inspired game that is also like this.

the Submachine series by artist Mateusz Skutnik also benefits from using pen and paper, although a few of the games include virtual notes as well. The later games in the series are more open ended and require you memorizing coordinates if you don't take notes. It also helps to write down which items you collect (potentially) go to which screens. It's a 2D point and click adventure game series.

Welcome to my favorite genre of game!

As they've already been mentioned before, I will second both La-Mulana (and though not mentioned, it's sequel), and FEZ.

The Witness didn't make me break out Pen and Paper, but it was definitely one I had to give my brain a break and come back to to look at things from a fresh angle.

Now for some previously unmentioned finds where your attention to detail will be rewarded. Not all will require notebooks. But there puzzles hidden in all of them.

Environmental Station Alpha is a Metroidvania.

Full Metal Furies is a side-scrolling beat-em up.

INSIDE is a side-scrolling platformer.

Inscryption is a deck-builder / puzzle room.

Factorio

Gotta keep track of production balance somehow..

Pretty much any 90s point and click adventure game made by Lucas arts, Sierra etc. No objective marker, no journal, you just wander around clicking things trying to mash items together. “Where did I see that symbol before?? flips through notebook Oh right!”

Myst. Surprised this wasn't mentioned yet.

Definitely Fez when you start looking beyond the golden cubes.

Keep Talking and Nobody Explodes has an entire manual that you should print out and put in a binder, and your manual monkeys will absolutely need pen and paper to help you defuse the bomb in front of you

Only 2 games that really made me break out pen and paper.

Myst 3 and Final Fantasy XII (The Great Crystal).

Secret World was a great modern horror MMO for a while there, and the investigation missions had some really complex puzzles that expected you do go online and do research into Egyptian dynasties and King James bible quotes and all kinds of other stuff. They dumbed down the amazing build system the game started with, but the core story skills still all be worth playing.

Original Metroid.

No notepad, but an excellent explorative puzzle that had me making and remaking theories the whole time: outer wilds. Several people also mentioned obra dinn

The new System Shock remake. I needed to draw a map of all elevator connections because Citadel station is extremely convoluted. Also, you get codes (or parts of codes) and instructions here an there, that you'll need later on.

Elite Dangerous. People have guides on how to do things like earning money fast, but those methods usually require a lot of thinking and planning with a notebook.

Maybe not my favorite game but one of the very few games I truly felt required pen and paper were some of the old Might & Magic games - most notably I think of the first 3 games.

Those were first person dungeon crawling RPGs. They didn't have, what later became termed "automaps", but what is now just a in-game map. So if you wanted to look at a map you had to either buy real life books they sold called Cluebooks which had maps printed in them or you had to pull out the graphing paper and get to drawing.

It wasn't just a limitation of the time, the games back then honestly treated it like a feature. I think it was in M&M3 that you could eventually cast the spell "Wizard Eye" and the entire point of the spell was to present to you a minimap of the surrounding area. NPCs and quests didn't put icons on your map (there was no map), you were given directions and had to figure out how to get there.

Subnautica forced me to draw a proper map. It was interesting.

It happened only one time, when playing Final Fantasy X, I really wanted to know what they were saying before finding all the Al Bhed primers. So I found a few NPC, took notepad and using a few letters found in the beginning, I was guessing what they were saying. It was quite satisfying and helpful, albeit easy.

La-mulana. It's one of those games that only has value if you play it blind and without a walkthrough. The game's platforming and combat is subpar at best and atrocious at worst, but the riddles and the mythology make up for it. I played it around 2008 on the "MSX" freeware version, and it took me 10 months and 2 new save files after getting stuck. You have no chances of completing that game without extensive notes.

Since you already said Tunic, I'll throw out Riven: The Sequel to Myst

I played it several months ago for the first time and my desk was completely littered with sticky notes, most of which would have been incomprehensible to anyone else

Not quite the same puzzley aspect but check out etrian Odyssey. It's premise essentially is that you have a dungeon crawler and you have to make the map yourself. There are tools in game for making the map as you go.

I don't think anything will ever beat Ultima IV for me in this regard.

Oh man, last one that made me do that was probably Zork III. I was hand-drawing my own maps to navigate that game. I miss those days.

A bit different but The Painscreek Killings. You're a reporter investigating an abandoned village where years ago a couple of murders happened. There is no set ending to the game, you can leave at any time and answer a bunch of questions to see how much of the mystery you have solved correctly, a bit similar to what Obra Dinn does. Until then you can more or less freely walk around (there's a rough order enforced by keys and hints) and figure out what's important. I've filled close to 20 pages with notes, relationship diagrams and a few sketches and still feel like I've seen maybe half of what's there.

EverQuest! I was pretty young back then, but I remember EQ not having a quest tracker back in the day. You'd talk to NPCs and have to keep track of what they were asking for.

System Shock 2. Just the perfect amount of non-handholding and thinking required without being cryptic or tedious.

I play Ocarina of Time randomizers using both a tracker and my own notes. That game is pretty huge, especially when things are shuffled around.

Honestly, Elden Ring. I kept a small notebook on the side to write down all the different bits I didn’t want to forget. Clues and quests and stuff like that. There were so many things if you pay attention and take care to try to piece together. It was really fun to come across something many hours later and then pull out the notebook to find my notes on it.

Signalis. Retro horror game with a really messed up plot; I had to write down radio codes and door diagrams in order to remember them.

Voices of the Void.

Writing down the dish names and codes for the reports is a lot more fun than I thought.

Mostly old point and click games like Sierra and Lucasarts things. Stuff where you can easily softlock yourself with 1 simple mistake.

Its old but I think fits, the original silent hill I needed a pad and paper at all times. Some puzzles were quite tricky.

Oxygen Not Included. Gotta compute the rate at which dupes consume resources to adjust production. It's so hard yet so satisfying. The dupes are extremely stupid though

I play a lot of old point and click games, and many of them are much easier with a solid note taking practice integrated into my play.

Dishonored 2!
Not the whole game, just a single level where you can avoid killing and sneaking by solving the Jindosh riddle.