[ci] Only notify after labeling (#32103)

---
[//]: # (BEGIN SAPLING FOOTER)
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with [ReviewStack](https://reviewstack.dev/facebook/react/pull/32103).
* __->__ #32103
* #32102

.github/workflows/compiler_discord_notify.yml

@@ -2,6 +2,7 @@ name: (Compiler) Discord Notify
 
 on:
   pull_request_target:
+    types: [labeled]
     paths:
       - compiler/**
       - .github/workflows/compiler_**.yml

.github/workflows/runtime_discord_notify.yml

@@ -2,6 +2,7 @@ name: (Runtime) Discord Notify
 
 on:
   pull_request_target:
+    types: [labeled]
     paths-ignore:
       - compiler/**
       - .github/workflows/compiler_**.yml

.github/workflows/shared_core_label.yml

@@ -1,41 +0,0 @@
-name: (Shared) Core Label
-
-on:
-  pull_request_target:
-
-env:
-  TZ: /usr/share/zoneinfo/America/Los_Angeles
-  # https://github.com/actions/cache/blob/main/tips-and-workarounds.md#cache-segment-restore-timeout
-  SEGMENT_DOWNLOAD_TIMEOUT_MINS: 1
-
-jobs:
-  core_label:
-    runs-on: ubuntu-latest
-    steps:
-      - uses: actions/checkout@v4
-      - name: Check if actor is maintainer
-        id: check_maintainer
-        uses: actions/github-script@v7
-        with:
-          script: |
-            const fs = require('fs');
-            const actor = '${{ github.actor }}';
-            const data = await fs.readFileSync('./MAINTAINERS', { encoding: 'utf8' });
-            const maintainers = new Set(data.split('\n'));
-            if (maintainers.has(actor)) {
-              console.log(`🟢 ${actor} is a maintainer`);
-              return true;
-            }
-            console.log(`🔴 ${actor} is NOT a maintainer`);
-            return null;
-      - name: Label PR as React Core Team
-        if: ${{ steps.check_maintainer.outputs.result }}
-        uses: actions/github-script@v7
-        with:
-          script: |
-            github.rest.issues.addLabels({
-              owner: context.repo.owner,
-              repo: context.repo.repo,
-              issue_number: ${{ github.event.number }},
-              labels: ['React Core Team']
-            });