I have tried all these things and none of them work. I tried calling Apple as well and they didn't seem to have any solutions, however, I see these comments on various sites, so I know the issue is not isolated to just me.
Essentially the pictures will not load on any of my devices (iPad, iPhone, iMac, or MacBook) and it will initially show a "tap to download" button which after hitting and it acting like it is downloading, simply will not download and ultimately becomes a thumbnail with a ?.
I have all my messages going back since I first got an iPhone, so its a large database of messages, but I have always backed it up, initially on my computer, then once upload to cloud was available, I did that as well, and then once iMessage backup was enabled, I let it back up to that, and the size of the file is representative of this.
As for space on my iPhone, I have the latest iPhone 12 Pro, and have PLENTY of space, so that shouldn't be an issue at all.
Any idea how to get it to start loading pictures again? I hate to suggest it, but does signing out of iCloud on my iPad, iPhone, MacBook, and iMac, such that iMessages is not enabled on any of those devices, and then enabling them one at a time again, have any logic at all? Seems like a lot of hassle (with having turn off find my phone, etc. etc. etc.) but I figured I would ask. Just seems like an Apple issue that isn't being addressed.