If your supervisor gave you an unviable project that was a dead end in honors or masters, do you think that they will write badly about you in a letter of recommendation to make themselves look good?
To be honest, if you intend to have this person write a letter of recommendation for you, I don't see any alternative but to talk to them about where you stand and how supportive they can be in a letter.
I doubt that anyone who wasn't a complete jerk would object to such a discussion. And having the discussion would give you valuable information about what you can expect. If they put you off or object to the question, then I'd suggest looking elsewhere for letters.
If the prof gave you an infeasible project (too easy or too hard) then they share in the outcome, though going back if it proves too easy is a good plan, though too late, now, to implement. My doctoral dissertation could have had a hundred proved theorems had I not warned my advisor that it was all trivial and signified nothing. It would have been nothing but "junk food" without substance.
Research is tricky since you are initially looking into the unknown void. For undergraduates it is especially tricky because of the time limitations on such things. The same may be true at the masters level if the degree is time limited. Some open questions in mathematics have remained so for a hundred years.
I suspect it has to do with why you thought the project was unviable and a dead end, and whether after all was said and done your mentor agrees with that or not.
I teach design courses, and very often a design doesn't work out the way students thought it should. This is fine. We shoot for a "proof or disproof of concept". At the end, we hope the students understand whether their design choice was a good idea or a bad idea, and whether their design process was working for or against them.
One of my favorite projects was an abject failure -- in that it didn't meet the needs of the process they were designing. In many other aspects, it was highly successful. The students opted for a high-risk design, and made a very compelling case why knowing whether that design worked or not was a valuable pursuit. They knew it was risky going in, and by the time they were done, we categorically understood why it would not work. Their process was fine. It would have been a very different story if they reached the same outcome, though they had misunderstood how risky their approach was (and should have), or if after all the effort, they still weren't completely sure whether it worked or not. This was the right kind of failure.
Somehow, this doesn't feel like how your project ran, but I could certainly be wrong about that.