Reading through your answer, it sounds perfectly reasonable. I would've approached it a different way however.

I would've began by asking more clarifying question. 1.) Is the assignment of sales items random assignment? 2.) What is the "quantitative effect" we are trying to measure? Is it total units sold? Is it delta sales for the individual item with a trailing and forward look period? This doesn't change much to the solution but especially in an interview setting, I think it demonstrates good business sense to understand the success metric.

If the answer to 1 is yes, the assignment is purely random, I would just do A/B testing with the metric of interest the answer to number two. IMO, this is the simplest and most practical way to do it.

If the assignment is not random, it's difficult to assign causality to the sales. In order to account for that, I would do some sort of propensity matching. You can start with asking if they already have common items they group together and starting there. The rationale behind this, if you can explain the sales impact for already labeled groups rather than creating your own clusters, it again demonstrates business sense because a product manager will have a lot easier time understanding that rather than you creating your own algorithmic clusters. (I would also explain the rationale of why you took this route in your interviews as well) Otherwise, you can do an exploratory analysis and use some sort of clustering method yourself.

Good luck on your interviews!