Embedding of list of objects
So, you want to make embeddings for sequences of items, and order doesn't make much sense. You don't have a specific objective, just want to retrieve embeddings with some conventional properties, such as natural clustering.
If you can train word2vec and take mean of item embeddings in a cart, you'll probably get noisy vectors. It doesn't work as well as expected, from my experience. I suggest that you try dimensionality reduction methods, such as NMF. Fit it with a sparse binary matrix of shape (num_samples, num_items). You'll get transformed vectors of desired dimensionality.
Then you might want to evaluate embeddings somehow. If don't have any quality metrics, you can either perform clustering to see how your embeddings form groups, or make nearest neighbour search queries by hand.
Good luck!