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 csesoc/deployment from this repo's workflow.

Changes

• replace the current deploy step flow with devsoc-unsw/deployment-dispatch-action@main
• 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

Context

This uses the shared devsoc-unsw/deployment-dispatch-action with explicit target inputs for csesoc/deployment on develop, because csesoc/deployment-dispatch-action does not exist.

Verification

• 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 for old major action refs and the missing steps.meta definition
• confirmed csesoc/deployment has .github/workflows/dispatch-image-update.yml on its default branch and that its manifest matcher accepts ghcr.io/csesoc/projects-discord-bot

[risu729]

Superseded by #224, which includes the same dispatch-action migration plus distinct qa/ptb image names to avoid cross-environment deployment updates.