I've done something similar for product designer interviews in past roles and at my current company: rather than any variation of take-home or design challenge (which are unethical and unhelpful), we ask candidates to do a design critique with us centred around a third-party product of their choice.

It gives us great signals into the things we care about in designers: communication skills, design and product thinking, their mindsets and approaches to thinking about and evaluating products and design, and even their craft.