I have this issue too.
I have my main library on another disk formated as BTRFS, but my games are still downloaded in ~/.local/share/Steam/steamapps/downloading, when I download bigger games my disk fills up completely, and the system crashes due to a lack of space.
So I have to stop the download, then shutdown steam completely and delete all the content inside the downloading folder.
Then I edit the game's manifest file saved on my main library adding:
"StagingFolder" "1"
This tells steam to use the correct "downloading" folder from my main library.
I hope this gets fixed soon because it is annoying to do when a game releases a big update or patch.
I seem to have the same problem as described here:
https://github.com/ValveSoftware/steam-for-linux/issues/12150
I also have steam libraries on 2 different partitions and steam uses a different partion for downloading than the one where the game is installed. Reinstalling the game works for the reinstall but does not change the downloading location and the error reappears with the next update.
OP fixed their issue by removing one of the libraries so steam must then have used the downloading folder in the correct library again. However, I would like to fix this issue without having to remove my library.
So I have steam and my game installed on partition A, but steam uses the downloading folder in my library on partition B for this games' updates and fails every time. Both partitions have over 100 GB free storage. Other games update without issues.
How do I make steam use the downloading folder on partition A instead? I have tried reinstalling the game, clearing the download cache, manually deleting the downloading folder, moving the contents of the downloading folder from B to A and restarting steam, but steam keeps using the downloading folder on partition B even though the game is on partition A.