Hey!
I assisted at my university's legal clinic during my final year and had similar doubts about whether to refer to it in interviews, as it didn't directly involve commercial law. What may be happening is that firms are stress-testing your motivation, rather than directly judging your prior experience. If they can't immediately see the link to commercial law, they may try to get this out of you through questions such as "why not public law?".
What helped me was framing the experience around the elements that are directly relevant to commercial practice, and I then explained why those elements motivated me to pursue commercial law overall. For example, things such as working closely with clients and using problem-solving skills to provide clear and practical advice. If you position it in a similar way, the experience will support a genuine interest in commercial law rather than detract from it, provided you are clear and convincing about why commercial law is the path you want to pursue
