Does iMessage in iCloud download all texts to my computer?

I have 142 gb of text messages saved in iCloud. When I look at my iPhone storage, only 7 gb are currently downloaded to the device (with the rest being stored in iCloud to be downloaded when necessary I'm assuming).

However, my 4-year-old MacBook has over 100 gb of messages downloaded. If I were to get a new Mac, would all 142 gb of texts be downloaded to the device (instantly taking up a bunch of storage) or would it be like the iPhone with only a small portion downloaded at a time?