For me this error was assets (animations) created in 4.26 and not compatible in 4.25. I try to export them from 4.26 and reimport in 4.25 in fbx. I got these errors when trying to save these animations.
I found that when retargeting these animations before closing Unreal they are saved but not non compatible version. So at least I can use my retargeted animation!
Hey! Did you fix problem?
In case anyone has this problem:
I had this issue because I had deleted a bunch of streaming actors when they were unloaded, and then I recreated them. old files existed still in folder structure, so I couldnt save newly created ones, which for some reason used same names.
old files which cause fail to save may exist already in folder:
“…\Unreal Projects\ProjectName\Content_ExternalActors_\Levels\LevelName\X\XX”
I checked date and time of one of left over old files.
Then I used windows search and deleted everything created from and after that time.
Then I was able to save my project as normal.
Might cause issues, do at own risk 
Thanks yeah, this happened for me in 5.2… went to the toilet came back to find the crash message and no unreal engine!! Reloaded and caried on working to get back to where I was, on try to save I had the same message. So I located the asset it said was only partially loaded and moved it to the desktop, then the project saved!
legend
I had the same error in Unreal 5.3 where i coudn’t save my Asset ‘…/…/…/…/cosmodome/Content/Sequence/LS_Prise_De_Vue_De_Haut_Lune.uasset’ cannot be saved as it has only been partially loaded, and i found out that it was because and old file named LS_Prise_De_Vue_De_Haut_Lune.uasset was corrupted so i just changed the name of the level sequence and it was able to save, dont know if it can be usefull but its gonna be here for someone if they need help.
I am getting this issue by simply duplicating an instance material (megascan) to assign to a different object. Then only changing the name in the content browser is the only way the new material can be saved which never happened to me before ever.
This is in 5.3 because I had to go back from 5.4 due to some weird light flickering issues and artifacts in the viewport and render and after trying a bunch of previous nvidia drivers the only thing left to try was going to the previous UE5 version.
So I had to create a new project from scratch in UE5.3 and when I started importing all my 3d assets again I ran to this issue not able to save instace materials after duplicating
Any idea why this is happening?