Client Credentials with the Local Connector?

[Radiergummi]

I want to use Dex in a local development environment as part of a Docker Compose stack. It's used by a service that needs an OAuth Authorization Server to connect to and request a token from; essentially Dex is a standin for our production IdP.

I have set this up using SQLite and the local connector:

compose.yaml

services:
  dex:
    image: dexidp/dex:v2.44.0-alpine
    restart: unless-stopped
    command: [ "dex", "serve", "/etc/dex/config.yaml" ]
    configs:
      - source: dex-config
        target: /etc/dex/config.yaml
    ports:
      - host_ip: "127.0.0.1"
        target: 5556
        published: 5556
        mode: host
        protocol: tcp
        app_protocol: http
        name: Dex IdP
    healthcheck:
      test:
        - CMD
        - wget
        - --quiet
        - --spider
        - http://localhost:5556/dex/.well-known/openid-configuration
      interval: 5s
      timeout: 3s
      retries: 5

configs:
  dex-config:
    # language=yaml
    content: |
      issuer: http://dex:5556/dex
      storage:
        type: sqlite3
        config:
          file: ":memory:"
      web:
        http: 0.0.0.0:5556
      oauth2:
        responseTypes:
          - code
        passwordConnector: local
      staticClients:
        - name: GraphQL API
          id: "${CLIENT_ID:-graphql-api}"
          secret: "${CLIENT_SECRET:-secret}"
          redirectURIs:
            - "http://localhost:4000/callback"
      enablePasswordDB: true
      staticPasswords:
        - email: "${USERNAME:-user}@dev.local"
          hash: "$2a$10$2b2cU8CPhOTaGrs1HRQuAueS7JTT5ZHsHSzYiFPm1leZck7Mc8T4W" # "password"
          username: "${USERNAME:-user}"
          userID: "00000000-0000-0000-0000-000000000001"

Now that works, but only using the password grant. Our application expects to be able to use client_credentials to request a token using, well, client credentials only.

Is this supported in Dex right now when using the local connector, or only for upstream IdPs (using token exchange)?