Majsmom, I’m by-no-means an expert on the matter—my mother just switched from Android on an outdated 4G plan to an iPhone 14 on a 5G plan and went through this. The issue for her revolved around one conversation in particular where a lot of pictures/videos/etc were shared, matching the pattern of many others here. Perhaps this might help:
Setting iCloud to “On” and then going to “iCloud Backup>>Back Up Now” would look like it was working, but was showing a message saying there isn’t enough space. I got the same message when I went through the iCloud settings and turned off everything except Shared Albums (under Photos), and Messages.
This didn’t seem to fix the problem for me. So I stopped a few things from using my internet so the phone would have as much Download speed as possible; I then brought up the conversation and left the wheel to spin away. Lo and behold, the text messages and barrage of pictures finally arrived.
However, after the text messages appeared, I noticed the storage used for Messages (in iCloud>>Manage Storage) had gone up. So, it may have been one, or it may have been both.
So, I recommend making sure you’re on a Wifi with a decent speed, without anyone streaming or downloading while trying to retrieve the messages. I also recommend having one of the conversations up, or at least the Messages app—this might be unnecessary, but I can see it losing priority if it’s not the focused app, or perhaps deleting the cache of the download. It could take hours if it’s a slow speed. If still nothing, perhaps try the original iCloud solution, but make sure only Shared Albums (under Photos) and Messages are switched on under iCloud settings, then repeat waiting for them to download. (Just FYI, it warns you about Safari settings and Notes, but her phone was fairly new, so those weren’t issues)
If still nothing, I’m making a guess that perhaps your conversations are actually exceeding iCloud’s minuscule 5GB for its free plan. There’s an upgraded plan, where it’s 50GB for $1 a month—and then there’s others that go even higher, up to $10, if you think that’s still not enough. It’s not much of a risk if it doesn’t work, but seems very-much worth it if it does work. It’s billed monthly, so just make sure to cancel before the next cycle. This is only a last resort, of course—I understand how stupid it sounds to throw money at something, blindly hoping it works, when it currently feels like it’s just giving you a spinning middle-finger.
I agree that this sucks, and you shouldn’t try to jump through this many hoops to have a functioning phone. By all means, you have the right to be angry, and I’d be frustrated too if this was happening to me—that’s why I shut down all my electronics just hoping for the conversation to load for my mom. The worst part is that is has no indication that anything is loading, or failing to load. The problem I think comes down to Androids not wanting to make it easy for people to switch to iPhone, and vice-versa. They want to make it frustrating to the point that you switch back.
Anyways, sorry for the long post. I just saw your message and hoped my experience might help get your conversations back in one piece. I see you posted this about a month ago, so perhaps it’s already been resolved. Either way, I really hope you get an early Christmas miracle, and you notice that all your old conversations and pictures are back very soon! Good luck!!