Is it frowned upon to obtain a recommendation letter from a recent Ph.D. graduate?
I wrote one or two recommendation letters as a graduate student, though only after encouraging the students to find someone else if at all possible.

My experience is in math, which may be different, but it's been that a letter from a PhD student counts for somewhat less. Prestige of the letter writer matters a bit, as does experience, and a PhD student generally doesn't have either.

It would be common in your situation, I think, to have the lead faculty member write the letter, but consult with the PhD student about what to say. (Or even to have the PhD student write portions of the letter and have the lead faculty member complete and sign the letter.)

When students have done a research project but the supervising faculty member doesn't write a letter, that can be a red flag. A letter from a PhD student helps, especially if it explains that they did most of the supervising, but it still raises questions.