This delivers on the title but I wonder if you could tweak it to make it an actual game without wildly overcomplicating it.

Maybe make the string much longer, like 10 bits, and the game only matches on substrings longer than 3. 000...000 would generally return no matches.

That's still probably solvable with superpermutations but wordle is "solvable" with a dictionary, so don't let perfect be the enemy of "better than 2 guess bordle"