It's common to have situations where you need to guess between two possibilities, and then you'll find out that one is wrong and you need to backtrack.
So I hope the algo you implement only excludes puzzles with more than one solution. As long as there is exactly one solution, it's completely logical and fair game.
This is a philosophical point about what's considered solveable. For example, in the sudoku community, there's this idea of bifurcation, which is when you get to a point in a puzzle where there are two options to take, and you step through each option manually until you figure out which one is correct, and backtrack if necessary.
You can do an entire puzzle this way (just keep on trying options and seeing if they work), but this is generally not on. If you build a puzzle that can only be solved this way, then you've built a bad puzzle, at least by the standards of the sudoku solving community. On the other hand, most complex or variant sudoku puzzles will have moments where there are two or three possibilities for a cell, and you need to look at the immediate effects of those possibilities to figure out which one is correct. So clearly some amount of bifurcation and backtracking is fine.
Fwiw, in the nonograms I've done in various apps, there's almost never a need to guess between different possibilities. I don't know if that's because the puzzle format itself is fairly constrained, or if the apps typically try to exclude these cases. But typically, it's always possible to see a next step, without needing to try things out and guess.
I really don't like the wording about multiple solutions not being logical. I get that instances where resolution doesn't lead you to the unique solution are annoying and don't scratch the right part of your brain, but I feel this audience could be more precise.
It's common to have situations where you need to guess between two possibilities, and then you'll find out that one is wrong and you need to backtrack.
So I hope the algo you implement only excludes puzzles with more than one solution. As long as there is exactly one solution, it's completely logical and fair game.