CI - Merge hooks (#4224)

# Description of Changes

Invoke a private workflow when a PR merges, so that we can do extra
follow-up actions.

# API and ABI breaking changes

None. CI only.

# Expected complexity level and risk

2

# Testing
- [x] When a PR merged with a corresponding private PR, I got a discord
notification:
<img width="543" height="70" alt="image"
src="https://github.com/user-attachments/assets/209347c3-57be-47d7-8d75-6154c9e222cb"
/>

- [x] When a PR merged without a corresponding private PR, no discord
notification

---------

Signed-off-by: Zeke Foppa <196249+bfops@users.noreply.github.com>
Co-authored-by: Zeke Foppa <bfops@users.noreply.github.com>

Author: bfops

.github/workflows/discord-posts.yml

@@ -20,6 +20,7 @@ jobs:
           sudo apt-get update
           sudo apt-get install -y gh
 
+      # TODO: Perhaps we should merge this into the public-pr-merge.yml workflow, now that that exists.
       - name: Send Discord notification
         env:
           DISCORD_WEBHOOK_URL: ${{ secrets.DISCORD_WEBHOOK_URL }}
@@ -69,3 +70,25 @@ jobs:
           # Use `jq` to construct the json data blob in the format required by the webhook.
           data="$(jq --null-input --arg msg "$message" '.content=$msg')"
           curl -X POST -H 'Content-Type: application/json' -d "$data" "${DISCORD_WEBHOOK_URL}"
+
+  invokePrivate:
+    runs-on: ubuntu-latest
+    if: github.event.pull_request.merged == true &&
+      github.event.pull_request.base.ref == 'master'
+    permissions:
+      contents: read
+    steps:
+      - name: Dispatch private merge workflow
+        uses: actions/github-script@v7
+        with:
+          github-token: ${{ secrets.SPACETIMEDB_PRIVATE_TOKEN }}
+          script: |
+            await github.rest.actions.createWorkflowDispatch({
+              owner: 'clockworklabs',
+              repo: 'SpacetimeDBPrivate',
+              workflow_id: 'public-pr-merge.yml',
+              ref: 'master',
+              inputs: {
+                public_pr_number: String(context.payload.pull_request.number),
+              }
+            });