Looking at my Photos library on the mac right now, and it says “Last synced 1 minute ago,” but the last photo I see that synced was 5 days ago. I’ve noticed this before too, but I blew it off at the time. All photos seem to sync up eventually, as I’m not missing any, but 5 days??? Come on, Apple…
I logged on to icloud.com and I see they are there. Just not on the mac. ¯_( ツ)_/¯
Like you said, iCloud syncs eventually. But five days seems excessive. Here’s some things Apple says to check.
This is a bugbear for me too. Never really got to the bottom of it and it’s not a consistent issue. Restarting affected devices usually sorts for me but shouldn’t be the case. Always gets there in the end but not really useful if you need them now.
Photos usually syncs quickly to my iMac, but I have started seeing a warning that “sync has been paused until your Mac cools down”. I have a late 2020 relatively high-spec Intel iMac 27". It runs perfectly and I do not have problems even when rendering quite large movie projects in Final Cut Pro. However, I have noticed that during the last few months the cooling fan is more active, and I have started getting that warning in Photos.
In contrast, iCloud Drive can take an inordinately long time to sync. I am still waiting for audio recordings I made with Ferrite on my iPad yesterday to appear in the folder on my iMac.
Thanks but there didn’t seem to be anything unique to the typical level 1 troubleshooting steps; it was only missing “try rebooting,” which probably cures more odd behavior than anything. That overheating issue seems to be for Intel macs too.
All that being said, I checked again today, and all the syncing is up to date, including the pictures I took just a few minutes ago. 
I’ve always suspected Apple‘s troubleshooting instructions are only designed to keep us busy and give iCloud more time to work. 
