Syncthing does not have permission to create directories in /volume1. I have no clue what those permissions mean, if you have access to a command line, run ls -ld /volume1 to get unix permissions.
Anyway you might get better support on a synology forum, as this is a synology, not syncthing specific problem.
Could not chdir to home directory /var/services/homes/admin: No such file or director
admin@DiskStation_01:/$ ls -ld /volume1
drwxr-xr-x 24 root root 4096 May 25 22:27 /volume1
admin@DiskStation_01:/$
The current permissions only allow the root user to create sub-directories below /volume1. Assuming (and hoping) that SyncThing isn’t running as root this is the reason for the error message.
To solve this, you could change owner/permissions of /volume1, but this might cause issues if this mountpoint was created by the Synology OS. I’d rather create a sub-directory and set permissions as needed, e.g., by changing its owner to the user running the SyncThing process.