How to download messages from iCloud to a backup

In iCloud settings on MacOS Monterey 12.2.1, there is a button next to "iCloud Storage" that is labeled "Manage...". When I click that and select "Messages" (because I want to manage iCould storage for Messages), the instructions state "If you want to stop using Messages and recover your iCloud storage, you can disable it on all your devices. You then have 30 days to download your messages." (emphasis added). That is what I would like to do, download my messages. Unfortunately, there is no method, button, instruction, or anything of the kind that supports downloading messages (that I can find). There are hints about downloading just the photos into Photos, but there is nothing about downloading messages.

I have saved my photos. Now I want to download my messages as promised on this window in iCloud Settings. How, precisely, do I do that? And please don't tell me that I have to continue to store them in iCloud, because that is obviously not what is being communicated in the above quoted text. I want to continue to use iCloud to share my current messages between my devices, and download and archive my old messages somewhere else so that I can free up storage space in iCloud.

I apologize for using so much bolding, but I have read other community questions on this topic and have not seen an answer that addresses the actual messages that exist in Messages. So I am trying to be very clear about what I am asking.

Thank you in advance.