Software Update Permissions error
I've seen errors like this after an Apply to enclosed items was done to the Macintosh HD.

/var/folders/zz/zyxvpxvq6csfxfn_n00000s0000068 shouldn't be owned by your user account, but by _softwareupdate (UID=200). I see errors about …n00000sb400002s (_spotlight=89) and …n00000sm00006d (_locationd=205) as well, which isn't a good sign.

You could just reset /var/folders/zz/zyxvpxvq6csfxfn_n00000s0000068 permissions to 200:200 with a chown -R (sudo chown -R 200:200 /var/folders/zz/zyxvpxvq6csfxvn_n00000s0000068). /var/folders itself should be owned by root.

Since you've removed it, you could recreate (might have to recreate the 0,T and C subfolders too…) it and set its ownership as above. You could do that now, and it might let software updates download, maybe even install. It also might not.

You could remove /var/folders, but I've seen a system that didn't like that. If the permissions on it are mangled and you'd like to try without it, I recommend renaming it in single user mode first.