chore(actions): replace deployment PAT with app dispatch

[risu729]

Summary

Use the shared deployment-dispatch-action in .github/workflows/docker.yml instead of directly checking out and editing devsoc-unsw/deployment from this repo's workflow.

Changes

• replace the current deploy step flow with devsoc-unsw/deployment-dispatch-action@a115e2ad9226805cd2588dc6fa5b7775991b141a
• rename the app credentials to vars.DEPLOYMENT_DISPATCHER_APP_ID and secrets.DEPLOYMENT_DISPATCHER_APP_PRIVATE_KEY
• switch GHCR publish authentication to github.token
• remove all remaining GH_TOKEN and old IMAGE_UPDATER_* references from the repo
• keep the existing workflow shape, runner selection, and action versions unless a change was required to remove GH_TOKEN or preserve packages: write for GHCR publishing

Verification

• yq eval '.' .github/workflows/docker.yml > /dev/null
• rg -n "\bGH_TOKEN\b|\bIMAGE_UPDATER_APP_ID\b|\bIMAGE_UPDATER_APP_PRIVATE_KEY\b" . -S -g '!node_modules' returns no matches
• actionlint -color .github/workflows/docker.yml still reports pre-existing baseline issues in some repos, such as old major action refs and missing steps.meta definitions