I was suffering this issue as well for a long while, but it's been resolved. I have a theory as to what was going on, but no proof and it may just be coincidence. But I'll add what I think happened and the resolution in case it sheds light on anyone else's situation.
My photos "sync paused" issue started when I upgraded my 256 GB iPhone X to a 128GB iPhone 13. I had over 150GB of music on my old iPhone, and that all attempted to sync over to the new iPhone, which obviously ran out of space since it was a lower capacity phone. In the settings on the new iPhone 13, I switched the Music app to Optimize Storage, and set it to only use 32 GB. That seemed to free up the storage, and I thought I was done. Shortly after I noticed the photos sync paused issue, and fought with that for a few weeks.
Sometime later, I noticed that the Music app had a very high background battery usage, even though I never used the app (41% shown in Settings > Battery > Battery Usage by App). Switching to the 10-day view, the Music app usage was consistently very high every day as far back as I could see. I went into the Music app > Downloaded, and noticed that it was stuck in some sort of download queue loop. There was an option to cancel all downloads, which I selected. I assume this stuck download state had been going on since I did the initial account transfer when setting up the new phone.
This was my "ah-ha" moment, and immediately checked the photos app. Took a few photos and they immediately synced to iCloud. Over the next few days, I did further tests with the phone plugged in, on a full battery, and on a nearly depleted battery. All tests passed and photos keep syncing automatically, without having to press any "resume syncing for 24 hours" button. So I'm fairly confident that it was the excessive background activity of the Music app that was blocking the iCloud photo sync.
