Running integration tests in CI (#504)

## Summary

This PR enables running integration tests in our CI pipeline. This
should help us make changes with greater confidence.

## Checklist
- [x] I have performed a self-review of my code
- [x] I have made corresponding changes to the documentation (in
https://github.com/dbt-labs/docs.getdbt.com) if required -- Mention it
here
- [x] I have added tests that prove my fix is effective or that my
feature works
- [x] New and existing unit tests pass locally with my changes

Author: DevonFulcher

.changes/unreleased/Under the Hood-20260107-155318.yaml

@@ -0,0 +1,3 @@
+kind: Under the Hood
+body: Running integration tests in CI
+time: 2026-01-07T15:53:18.336434-06:00

.github/workflows/run-checks-pr.yaml

@@ -51,6 +51,33 @@ jobs:
       - name: Run tests
         run: task test:unit
 
+  # runs the integration tests
+  integration-test:
+    name: Integration test
+    runs-on: ubuntu-24.04
+    permissions:
+      contents: read
+    needs:
+      - check
+    steps:
+      - name: checkout code
+        uses: actions/checkout@08eba0b27e820071cde6df949e0beb9ba4906955
+      - name: setup python
+        uses: ./.github/actions/setup-python
+        id: setup-python
+      - name: Install go-task
+        run: sh -c "$(curl --location https://taskfile.dev/install.sh)" -- -d -b /usr/local/bin
+      - name: Run tests
+        env:
+          DBT_HOST: ${{ vars.DBT_HOST }}
+          MULTICELL_ACCOUNT_PREFIX: ${{ vars.MULTICELL_ACCOUNT_PREFIX }}
+          DBT_TOKEN: ${{ secrets.DBT_TOKEN }}
+          DBT_ACCOUNT_ID: ${{ vars.DBT_ACCOUNT_ID }}
+          DBT_PROD_ENV_ID: ${{ vars.DBT_PROD_ENV_ID }}
+          DBT_DEV_ENV_ID: ${{ vars.DBT_DEV_ENV_ID }}
+          DBT_USER_ID: ${{ vars.DBT_USER_ID }}
+        run: task test:integration
+
   # validates documentation is up to date
   validate-docs:
     name: Validate tool docs