Messages on Mac not storing in iCloud

The physical storage on my Mac is almost full, and nearly half of it is being taken up by Messages. I've tried to save space by turning on Messages in iCloud for the Mac, and while they are being stored in the cloud, they are doing so via my iPhone, all of the Message conversations and attachments are still being stored locally on my Mac. I've tried everything I can think of to fix it and nothing has worked.

I'm running macOS Sequoia 15.5, but this has been happening for many updates now.

I also still want to be able to use Messages on my Mac and have them be synced to the cloud, I just do not want the entirety of them to be physically stored on my Mac.