It’s important to separate not having the specific design solution to a specific problem from not having solutions to closely related problems. We don’t know what the mass budget etc would look like for an interstellar colony ship.
On the other hand several known designs mostly worked for humans to the point where using them would dramatically reduce the supplies needed for a long trip. But, none of them where operating on a zero G interstellar mission.
Biosphere 2 for example depended on sunlight which would be missing, but they provided sufficient calories across several months which means it was also generated enough oxygen assuming it had been setup properly to begin with. They had a huge range of other their issues, and you would need a vastly larger population and much higher efficiency for such a trip. But, from what amounted to a publicity stunt it was surprisingly close to a working solution.
https://en.wikipedia.org/wiki/BIOS-3 on the other hand was a far less ambitious project that was much closer to a practical design even if they imported food and the longest experiment was 180 days, it was actually using artificial lights.
PS: A more significant question is how to design hardware systems that could last for such a trip and what it would take to sustain things at the other side.