chore(tests): turn off dogweb CI runs (#11414)

This change disables dogfooding CI runs triggered from this repo,
because they currently cost more than the benefit they provide.

## Checklist
- [x] PR author has checked that all the criteria below are met
- The PR description includes an overview of the change
- The PR description articulates the motivation for the change
- The change includes tests OR the PR description describes a testing
strategy
- The PR description notes risks associated with the change, if any
- Newly-added code is easy to change
- The change follows the [library release note
guidelines](https://ddtrace.readthedocs.io/en/stable/releasenotes.html)
- The change includes or references documentation updates if necessary
- Backport labels are set (if
[applicable](https://ddtrace.readthedocs.io/en/latest/contributing.html#backporting))

## Reviewer Checklist
- [x] Reviewer has checked that all the criteria below are met
- Title is accurate
- All changes are related to the pull request's stated goal
- Avoids breaking
[API](https://ddtrace.readthedocs.io/en/stable/versioning.html#interfaces)
changes
- Testing strategy adequately addresses listed risks
- Newly-added code is easy to change
- Release note makes sense to a user of the library
- If necessary, author has acknowledged and discussed the performance
implications of this PR as reported in the benchmarks PR comment
- 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)

(cherry picked from commit d45dd33)

.gitlab-ci.yml

@@ -2,10 +2,8 @@ stages:
   - package
   - tests
   - shared-pipeline
-  - dogfood
   - benchmarks
   - macrobenchmarks
-  - dogfood
   - release
 
 variables:
@@ -29,7 +27,6 @@ include:
   - local: ".gitlab/package.yml"
   - local: ".gitlab/tests.yml"
   - local: ".gitlab/macrobenchmarks.yml"
-  - local: ".gitlab/dogfood.yml"
   - local: ".gitlab/release.yml"
 
 package-oci: