chore(actions): replace deployment PAT with app dispatch

[risu729]

Summary

Backport the deployment dispatch workflow change from develop to projects-bot so this branch stops using the legacy PAT-based deployment update flow as well.

Changes

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

Context

This backport keeps projects-bot aligned with the main branch workflow change and targets csesoc/deployment on develop through the shared dispatch action.

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 the same 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Superseded by #225, which includes the same dispatch-action migration plus distinct qa/ptb image names to avoid cross-environment deployment updates.