ci(debugging): change di backend repo to run dogfood pipelines [backport 1.17] (#6494)

Backport 79ddf54 from #6483 to 1.17.

Runs di pipelines in a different repo.

Testing: pipeline runs automatically on merge and release commits.
Failing pipelines will trigger alerts.

## Checklist

- [x] Change(s) are motivated and described in the PR description.
- [x] Testing strategy is described if automated tests are not included
in the PR.
- [x] Risk is outlined (performance impact, potential for breakage,
maintainability, etc).
- [x] Change is maintainable (easy to change, telemetry, documentation).
- [x] [Library release note
guidelines](https://ddtrace.readthedocs.io/en/stable/releasenotes.html)
are followed. If no release note is required, add label
`changelog/no-changelog`.
- [x] Documentation is included (in-code, generated user docs, [public
corp docs](https://github.com/DataDog/documentation/)).
- [x] Backport labels are set (if
[applicable](https://ddtrace.readthedocs.io/en/latest/contributing.html#backporting))

## Reviewer Checklist

- [x] Title is accurate.
- [x] No unnecessary changes are introduced.
- [x] Description motivates each change.
- [x] Avoids breaking
[API](https://ddtrace.readthedocs.io/en/stable/versioning.html#interfaces)
changes unless absolutely necessary.
- [x] Testing strategy adequately addresses listed risk(s).
- [x] Change is maintainable (easy to change, telemetry, documentation).
- [x] Release note makes sense to a user of the library.
- [x] Reviewer has explicitly acknowledged and discussed the performance
implications of this PR as reported in the benchmarks PR comment.
- [x] Backport labels are set in a manner that is consistent with the
[release branch maintenance
policy](https://ddtrace.readthedocs.io/en/latest/contributing.html#backporting)

Co-authored-by: Oskar Jung <[email protected]>
Co-authored-by: Emmett Butler <[email protected]>

Author: 3 people

.gitlab-ci.yml

@@ -60,7 +60,7 @@ deploy_to_di_backend:automatic:
     - if: '$CI_COMMIT_BRANCH == $CI_DEFAULT_BRANCH'
       when: on_success
   trigger:
-    project: DataDog/debugger-backend
+    project: DataDog/debugger-demos
     branch: main
   variables:
     UPSTREAM_PROJECT_ID: $CI_PROJECT_ID
@@ -76,7 +76,7 @@ deploy_to_di_backend:manual:
     - when: manual
       allow_failure: true
   trigger:
-    project: DataDog/debugger-backend
+    project: DataDog/debugger-demos
     branch: main
   variables:
     UPSTREAM_PROJECT_ID: $CI_PROJECT_ID