GH-1244: Move integration tests to separate workflow (#1245)

## What's Changed

Move the `integration` job from `test.yml` into its own
`integration.yml` workflow.

The new workflow uses top-level `paths` filters, so integration tests
run only when changes affect relevant code or build inputs.
This should also help to reduce the amount of runner time. Topic
initially triggered in the [mailing
list](https://lists.apache.org/thread/drf0o5kzg1zfmok7gc09k8qz8hh9ymvh)

Closes #1244
diff --git a/.github/workflows/integration.yml b/.github/workflows/integration.yml
new file mode 100644
index 0000000..3872d03
--- /dev/null
+++ b/.github/workflows/integration.yml
@@ -0,0 +1,127 @@
+# Licensed to the Apache Software Foundation (ASF) under one
+# or more contributor license agreements.  See the NOTICE file
+# distributed with this work for additional information
+# regarding copyright ownership.  The ASF licenses this file
+# to you under the Apache License, Version 2.0 (the
+# "License"); you may not use this file except in compliance
+# with the License.  You may obtain a copy of the License at
+#
+#   http://www.apache.org/licenses/LICENSE-2.0
+#
+# Unless required by applicable law or agreed to in writing,
+# software distributed under the License is distributed on an
+# "AS IS" BASIS, WITHOUT WARRANTIES OR CONDITIONS OF ANY
+# KIND, either express or implied.  See the License for the
+# specific language governing permissions and limitations
+# under the License.
+
+name: Integration
+
+on:
+  push:
+    branches:
+      - '**'
+      - '!dependabot/**'
+    tags:
+      - '**'
+    paths:
+      - '.github/workflows/integration.yml'
+      - '**/pom.xml'
+      - 'c/**'
+      - 'ci/scripts/**'
+      - 'compose.yaml'
+      - 'flight/**'
+      - 'format/**'
+      - 'testing/data/**'
+      - 'vector/**'
+  pull_request:
+    paths:
+      - '.github/workflows/integration.yml'
+      - '**/pom.xml'
+      - 'c/**'
+      - 'ci/scripts/**'
+      - 'compose.yaml'
+      - 'flight/**'
+      - 'format/**'
+      - 'testing/data/**'
+      - 'vector/**'
+
+concurrency:
+  group: ${{ github.repository }}-${{ github.head_ref || github.sha }}-${{ github.workflow }}
+  cancel-in-progress: true
+
+permissions:
+  contents: read
+
+env:
+  DOCKER_VOLUME_PREFIX: ".docker/"
+
+jobs:
+  integration:
+    name: AMD64 integration
+    runs-on: ubuntu-latest
+    timeout-minutes: 60
+    steps:
+      - name: Checkout Arrow
+        uses: actions/checkout@v7
+        with:
+          fetch-depth: 0
+          repository: apache/arrow
+          submodules: recursive
+      - name: Checkout Arrow Rust
+        uses: actions/checkout@v7
+        with:
+          repository: apache/arrow-rs
+          path: rust
+      - name: Checkout Arrow nanoarrow
+        uses: actions/checkout@v7
+        with:
+          repository: apache/arrow-nanoarrow
+          path: nanoarrow
+      - name: Checkout Arrow .NET
+        uses: actions/checkout@v7
+        with:
+          repository: apache/arrow-dotnet
+          path: dotnet
+      - name: Checkout Arrow Go
+        uses: actions/checkout@v7
+        with:
+          repository: apache/arrow-go
+          path: go
+      - name: Checkout Arrow Java
+        uses: actions/checkout@v7
+        with:
+          path: java
+      - name: Checkout Arrow JavaScript
+        uses: actions/checkout@v7
+        with:
+          repository: apache/arrow-js
+          path: js
+      - name: Free up disk space
+        run: |
+          ci/scripts/util_free_space.sh
+      - name: Cache Docker Volumes
+        uses: actions/cache@v6
+        with:
+          path: .docker
+          key: integration-conda-${{ hashFiles('cpp/**') }}
+          restore-keys: integration-conda-
+      - name: Setup Python
+        uses: actions/setup-python@v6
+        with:
+          python-version: 3.12
+      - name: Setup Archery
+        run: pip install -e dev/archery[docker]
+      - name: Execute Docker Build
+        run: |
+          source ci/scripts/util_enable_core_dumps.sh
+          archery docker run \
+            -e ARCHERY_DEFAULT_BRANCH=main \
+            -e ARCHERY_INTEGRATION_TARGET_IMPLEMENTATIONS=java \
+            -e ARCHERY_INTEGRATION_WITH_DOTNET=1 \
+            -e ARCHERY_INTEGRATION_WITH_GO=1 \
+            -e ARCHERY_INTEGRATION_WITH_JAVA=1 \
+            -e ARCHERY_INTEGRATION_WITH_JS=1 \
+            -e ARCHERY_INTEGRATION_WITH_NANOARROW=1 \
+            -e ARCHERY_INTEGRATION_WITH_RUST=1 \
+            conda-integration
diff --git a/.github/workflows/test.yml b/.github/workflows/test.yml
index 853b7ce..653b16f 100644
--- a/.github/workflows/test.yml
+++ b/.github/workflows/test.yml
@@ -147,72 +147,3 @@
         env:
           DEVELOCITY_ACCESS_KEY: ${{ secrets.DEVELOCITY_ACCESS_KEY }}
         run: ci/scripts/test.sh . build jni
-
-  integration:
-    name: AMD64 integration
-    runs-on: ubuntu-latest
-    timeout-minutes: 60
-    steps:
-      - name: Checkout Arrow
-        uses: actions/checkout@v7
-        with:
-          fetch-depth: 0
-          repository: apache/arrow
-          submodules: recursive
-      - name: Checkout Arrow Rust
-        uses: actions/checkout@v7
-        with:
-          repository: apache/arrow-rs
-          path: rust
-      - name: Checkout Arrow nanoarrow
-        uses: actions/checkout@v7
-        with:
-          repository: apache/arrow-nanoarrow
-          path: nanoarrow
-      - name: Checkout Arrow .NET
-        uses: actions/checkout@v7
-        with:
-          repository: apache/arrow-dotnet
-          path: dotnet
-      - name: Checkout Arrow Go
-        uses: actions/checkout@v7
-        with:
-          repository: apache/arrow-go
-          path: go
-      - name: Checkout Arrow Java
-        uses: actions/checkout@v7
-        with:
-          path: java
-      - name: Checkout Arrow JavaScript
-        uses: actions/checkout@v7
-        with:
-          repository: apache/arrow-js
-          path: js
-      - name: Free up disk space
-        run: |
-          ci/scripts/util_free_space.sh
-      - name: Cache Docker Volumes
-        uses: actions/cache@v6
-        with:
-          path: .docker
-          key: integration-conda-${{ hashFiles('cpp/**') }}
-          restore-keys: integration-conda-
-      - name: Setup Python
-        uses: actions/setup-python@v7
-        with:
-          python-version: 3.12
-      - name: Setup Archery
-        run: pip install -e dev/archery[docker]
-      - name: Execute Docker Build
-        run: |
-          source ci/scripts/util_enable_core_dumps.sh
-          archery docker run \
-            -e ARCHERY_DEFAULT_BRANCH=main \
-            -e ARCHERY_INTEGRATION_TARGET_IMPLEMENTATIONS=java \
-            -e ARCHERY_INTEGRATION_WITH_DOTNET=1 \
-            -e ARCHERY_INTEGRATION_WITH_GO=1 \
-            -e ARCHERY_INTEGRATION_WITH_JAVA=1 \
-            -e ARCHERY_INTEGRATION_WITH_JS=1 \
-            -e ARCHERY_INTEGRATION_WITH_NANOARROW=1 \
-            -e ARCHERY_INTEGRATION_WITH_RUST=1 \
-            conda-integration