In the sentence "ensembles that feel totally put-together", "put-together" is the same as "match", like "matching ensembles"?

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No, it doesn't mean matching (matching means being the same color or pattern). Some parts of the ensemble may match, but more importantly, they look good together. They complement each other. The necklace looks good with the blouse and the belt, but it may match it or not. The shoes look good with the pants, but they don't need to match. When all of the parts go well with each other, the ensemble is totally put-together.
It usually isn't good to have too many matching things in an ensemble. That is called "matchy-matchy", and often doesn't look good.
So maybe the ensemble was a white blouse with black pants and red shoes, and a chunky silver necklace with a hounds tooth jacket. Nothing matches, but it all looks good together, so it is is well put together.