Build docker image on PRs that touch the docker files (#4374)

Author: jesserockz

.github/workflows/docker.yml

@@ -9,6 +9,11 @@ on:
       - requirements.txt
       - Dockerfile
       - .github/workflows/docker.yml
+  pull_request:
+    paths:
+      - requirements.txt
+      - Dockerfile
+      - .github/workflows/docker.yml
 
 permissions:
   contents: read
@@ -34,11 +39,13 @@ jobs:
         uses: docker/setup-buildx-action@v3
       -
         name: Login to DockerHub
+        if: github.event_name != 'pull_request'
         uses: docker/login-action@v3
         with:
           username: ${{ secrets.DOCKER_USER }}
           password: ${{ secrets.DOCKER_PASSWORD }}
       - name: Login to GitHub Container Registry
+        if: github.event_name != 'pull_request'
         uses: docker/login-action@v3
         with:
           registry: ghcr.io
@@ -50,7 +57,7 @@ jobs:
         uses: docker/build-push-action@v6
         with:
           context: .
-          push: true
+          push: ${{ github.event_name != 'pull_request' }}
           platforms: linux/amd64,linux/arm64
           tags: |
             esphome/esphome-docs:latest