When folks encounter a video game challenge that requires a high degree of mechanical skills, like a boss fight in a Devil May Cry or Bayonetta, I find that they are generally more willing to try and try again or even maybe admit they are not skilled enough to do it. When it comes to puzzles though... I've observed that many players do not like the idea they couldn't solve them. They will call them bullshit. "How was I supposed to figure this out?" Puzzles test your logic reasoning skill. In our society we have a tendency to associate that particular skill with the completely fake concept of intelligence. So when you can't solve something, it's like being told to your face that you're not very smart. Just go on the comments of a solution video for any of the trickier Baba is You puzzles. You'll find plenty of people complaining it was unintuitive or the game made them feel stupid.

But here's the thing. I firmly believe puzzle solving has nothing to do with "intelligence". It's a skill, and like any other skills, it can be learned and honed with a lot of practice. No one expects a player new to fighting games to be able to win a tournament without first learning and practicing the fundamentals. Why should it be any different for logic puzzles?

Here are a few things that personally helped my puzzle solving skills:

all of this, but i desperately need to add that you are absolutely just allowed to trial and error things to feel out the me mechanics and develop an intuitive sense of an unknown system, then refine that to an understanding

this is a drum i will bang on all day

we're conditioned against doing this so hard almost from day one! i need you to understand that all of our education and formative experiences and job training run counter to this!

if you think about how we're taught to learn things from literally before we are able to read or write or reason about numbers, someone sits us down and tells us how to do a thing. we're told to maybe repeat it an annoying number of times in isolation with different words or numbers (nobody likes this) and no feedback, then we're tested on it

if you get something wrong, you get your answer marked by the big shameful red pen and a bad grade. at no point is there ever a feedback step where you're shown how you made a mistake and are given the opportunity to understand your error and correct it, in a context where this is seen as a positive and rewarding step

this is critical! it's a fundamental building block of human knowledge! people our culture typically portrays as "smart" are doing this all the time! so much of our collective knowledge and understanding is not built on the perfect synthesis of new ideas in a vacuum and "Eureka!" moments, but by the willingness to be repeatedly incredibly wrong until we understand enough that we start being somewhat less wrong¹

and that's kind of the energy i hope people can bring to puzzle games, or any other game with a challenge they can overcome by understanding, or many other non-game fields you might encounter

1. obviously like how puzzles often have a common history and design language that you can learn to better understand them, im not suggesting that it makes sense to trial and error everything from the ground up. there's usually some kind of common reference you can use as building blocks to get started!

These aren't mutually exclusive, but in my experience, people tend to be naturally inclined toward one or two of them, and different puzzle games tend to reward some more than others.

A few broad methods:

• Systematizing. This is what most people think of when they think of puzzle-solving. Itemize the rules and make logical conclusions based on them. Generalize the specific puzzle to a broader kind of puzzle, and figure out how the general solution applies. (The original poster here very clearly enjoys systematizing.) This tends to be seen as the "right" way to solve puzzles, but it's one of many.

• Experimentation, aka "fuck around and find out." Try things until you get an outcome that surprises you, yields fruit, or is just different from other outcomes you've seen. (The second poster here very clearly enjoys experimentation.) Adventure games tend to reward experimentation. So do games where there are a lot of new interactions to discover. (I'm pretty sure that at least half of the levels I solved in Patrick's Parabox hinged on my doing something and thinking "wait, what just happened?")

• Observation, aka noticing clues. Puzzles are artificial environments. Someone designed them. Things are the way they are for a reason, and an important puzzle-solving skill is the skill of looking at a puzzle's initial state and noticing things that look kind of sus.

Since the OP mentions Baba Is You, I'll use it as an example. Here is one of the late-game levels, "VIP Area." Its solution doesn't rely on any quirks or logical extensions of the rules -- or at least none that you haven't already seen if you've reached this level. The solution relies on you noticing a few unusual things about the layout. See if you can spot them:

The first important tile is this:

Notice how the surrounding wall is completely smooth and uniform -- except for this one little gap, which just so happens to be near a bunch of other objects and accessible by you. That's odd! Even if you know absolutely nothing else about the solution, you can guess that it will probably involve doing something with this weird, conspicuous gap.

There are a couple other things to notice. You have a single-tile wall just hanging out by itself, and you have a "tunnel" of three tiles near the bottom. These aren't there just to look cool. They are there for a reason.

(Again, these puzzle-solving methods aren't mutually exclusive. For instance, you're probably not solving this level if you didn't previously solve Prison, since the basic maneuvers here are similar. And if you figured out how to position yourself in the right place by doing something more organized than messing around, that's cool; I definitely didn't.)

These posts are great and I don't want to contradict anything they've said, but add a few points:

• "Lateral leaps" are another ingredient of puzzle design, most commonly used by old adventure games. Puzzles that lean on these often bend or break established rules, or carve out special cases, deliberately cutting across the lines you might draw in your head trying to map and "systematize" the design space, thinking deductively etc. When they're designed well, they feel like a well-told joke. When designed poorly they feel obnoxious and arbitrary.
• This is another case where I think understanding games as a web of interrelated creative traditions is useful. There are so many different puzzle design aesthetics and they each leverage very different kinds of thinking, and are aimed at a wide range of creative goals: storytelling, humor, learning, traditional "brain teasing", the sort of mind-expanding "think about this thing in a way you never have before" (I don't have a good term for these haha) revelations, etc. Because people get very psychologically invested in their own sense of "intelligence" - because our society basically tells you that you are worthless if you're not smart, and will starve to death! - they develop weird superiority complices around what types of puzzle they feel is the best, ie the "smartest". But it's all just art, and pretending there's some objectively "best" form is silly.
• Intelligence is fake. Which is to say, what we call "intelligence" is really just a massive bag of different capabilities, frameworks for thinking, knowledge domains, that each individual builds to varying degrees throughout their life. The people who are most obsessed with measuring intelligence are eugenicists and heyyy, maybe don't drink too much of their ideology! We like to feel smart, puzzles in games are an enjoyable way to poke different parts of our brains, but it's worth acknowledging that that feeling is a social-political domain with some real stakes for how different people are treated and what kinds of human experience, and labor, are valued or not valued.