Pre-covid during my split stays I would drag my luggage down to concierge and get it tagged and they would transport it. Then later that evening at my second hotel I'd call the new concierge and tell them I'd arrived so they would deliver it to my room. If this is how they still do it, expect to run on slow as molasses Disney time. Nothing will be quick. You will get annoyed waiting, but your stuff will eventually arrive.
If you aren't patient, get a Lyft/Uber and transport it yourself.