Where does Mac Messages store older Attachments?

I'm looking for one specific photograph, a jpg taken on my iPhone, which I know was sent to my partner over Messages, towards the end of 2019. I don't have it in what used to be Camera Roll on the phone nor in Photos.app on phone or Mac, so I'm going to have to dig it out from Messages.
I thought this was going to be a few minutes' job. I started by scrolling back in Messages, but then realised it would be quicker to find their storage location & sort by date… neither was successful.
If I scroll back a Messages conversation, then for the past six months or so I can see all attachments, pictures etc in-line as normal.

Once I get past that then they've apparently been archived somewhere & I can't find where. I have never 'cleaned' this conversation manually. This appears to be some automatic action taken without my knowledge. I could imagine my phone would do that to save space, but I didn't expect it on the Mac.

If I click on any of those down arrows, the picture will reload. This, as you can imagine, is not the fastest way to find a specific photo :\
If I search in Finder, Kind: jpeg image inside the Attachments folder at ~/Library/Containers/com.apple.iChat/Data/Library/Messages/Attachments I see only the same images as are already inlined. After I refetch an older one, it then appears at today's date.

^{Click for full size}

Searching the entire drive from Finder gives no other clues.
Using EasyFind to search hidden locations & packages etc for img_ reveals nothing more. BTW, I am not searching for _DSD files, they're from my "proper" photos.

My Messages are synced over iCloud between Mac & iPhone, though very little else is. I don't have my Photos on there, for instance. The only app I sync on iCloud Drive is Maps, nothing else. I sync things like Contacts, Calendars etc, not "multimedia" of any sort, so I don't expect the repository to be iCloud.

Are these images really held in iCloud, even though I haven't asked for them to be?

I am in no way short of data space, 1TB SSD boot drive, only half full & 12TB of other drives in this Mac. I have none of the iCloud Storage Management options enabled.

macOS 10.14.6 (latest this Mac can run) on Mac Pro 5,1.

Solution 1:

After comments

It does appear that these are shuffled off to iCloud, whether you want them to be or not.
From the Details button, top right, then scroll right down - rather blurred picture to demonstrate

Clicking that Download restores them to their correct location. How long before it decides to remove them again I've yet to discover.