How can I monitor docker volume usage?
I'd recommend a temporary container for this. It will work on just about any version of docker, and supports named volumes with non-default settings, e.g. that store data on remote systems (e.g. NFS) or modify the bind mound settings to use another folder.

A simple example is:

$ docker container run --rm -v "${volume_name}:/volume" -w /volume busybox df -P .
Filesystem           1024-blocks    Used Available Capacity Mounted on
/dev/..........              898086280 350169736 502226484  41% /volume


You can parse that output or reformat with the df command as appropriate for your use case. The busybox version of df will have fewer options than you may be used to:

$ df --help
BusyBox v1.31.1 (2019-12-23 19:20:27 UTC) multi-call binary.

Usage: df [-PkmhTai] [-B SIZE] [FILESYSTEM]...

Print filesystem usage statistics

        -P      POSIX output format
        -k      1024-byte blocks (default)
        -m      1M-byte blocks
        -h      Human readable (e.g. 1K 243M 2G)
        -T      Print filesystem type
        -a      Show all filesystems
        -i      Inodes
        -B SIZE Blocksize