A couple of times when doing crosswords in Puzzmo I've ended a puzzle with one or two letters missing because I didn't know either of the across or down clues for those letters. At this point I'd use the hints or just enter random letters until it gives me the clear, only to realise upon getting it that it's something I definitely could have worked out on my own.
Recently when playing this game with puzzles in it I got stuck on a puzzle, figured that because the rest of the game wasn't that great that the solution to the puzzle probably wasn't anything clever, looked up a walkthrough on Steam, and found that the solution was in fact kind of bullshit; it was one of those puzzles where there are a lot of potential things you could do and one of them just so happens to be correct. When I got stuck on a later puzzle I went for the walkthrough much quicker and found that the answer to this one was extremely obvious, I just failed to notice something that I really should have.
Pencil-and-paper logic puzzles traditionally have an unwritten rule that the puzzle must have only one possible solution. Some puzzles are much easier if you assume this rule is followed, and suspecting that it isn't can lead you to make incorrect guesses about the puzzle which take a lot of time to fix.
I think these are all kind of the same problem: solving puzzles requires you to trust that you actually can solve the puzzle, that the puzzle has an interesting solution, and that the puzzle is well-constructed. If you're missing any of these things you might start doing things that make it harder to think through the puzzle (wild guessing, thoughtless trial and error, or just giving up). More fundamentally, I think, solving a puzzle requires you to trust that you'll be rewarded for attempting to do so, with an interesting solution that you're eventually able to find.
How do you develop this trust as a puzzle-solving skill? You can get more confident in your ability by just doing more puzzles but I'm not sure how to get more confident in the quality of the puzzles you're trying to solve. Then again, should you be? Caving and giving up might be the right move if a puzzle is truly unreasonable. This reminds me of this long post about a very long hint-free playthrough of La-Mulana, a game which you could probably say to be unreasonable to complete without hints. Maybe the true meta-puzzle for every puzzle is knowing how much to trust the puzzle, so you can make a good decision on when to give up.
On the other hand, how do puzzle designers help with this? I'm reminded of a couple experiences I had at escape rooms: I once had a much harder time on a puzzle than I maybe should have because I thought they'd set it up wrong, that there was some vital object missing from the room, and once my whole group had a very hard time with a puzzle because it was actually set up wrong: a monitor that would display some vital clue was broken and they hadn't noticed. I suspected something wrong in the first case because the room seemed kind of... shonky.1 Good escape rooms inspire trust in their setup by improving everything else about the experience: their theming, the overall quality of their puzzles,2 so on. I have no idea how they actually make sure they set everything up correctly, but I can at least see how they make you believe they have.
I think some logic puzzles remind you of the "unique solution" rule, so less experienced puzzlers can make use of it and more experienced puzzlers have a bit more trust they did it right (I'm sure this is a thing but I can't think of any examples of it. They should do this okay). Puzzmo's crosswords have this "Standards" tab that affirms that they follow some typical crossword construction rules and lets you know what to expect. Some puzzles (e.g ABDEC, LOK) credit their playtesters up-front, as if to say, "look, we play-tested this, you can trust that the puzzles are good".3
And to make players more confident in themselves... Void Stranger says "If a puzzle seems impossible, get some rest" on the Steam page, and this reads to me as a way of encouraging players to not give up even when they think they can't solve a puzzle. Or maybe Void Stranger just does some nonsense with your computer's clock, I don't know. I should really just play the game.
1: I think these were both Escape Hunt franchises. Forget all the stuff about puzzles, this is actually a post about escape rooms: in all my experience, Escape Hunt rooms average out to being just okay. There are some really good escape rooms out there, they just tend not to be multinational franchises. Be suspicious of escape rooms that don't have clear photos of their room interiors online; if their theming and set design was actually any good, they'd be showing it off. Really good escape rooms can share photos without spoiling anything at all.
2: Escape room designers please stop using logic grid puzzles (or really any sort of pure logic puzzle you can turn into a logic grid puzzle), they're not really possible to solve collaboratively and just kind of lock up the one guy in the room who's the best at logic puzzles for a few minutes.
3: Maybe this is why, months later, I believe that the solution to that puzzle in ABDEC will somehow eventually just come to me.