ci: do not block on downstream dogweb job [backport 2.10] (#10415)

Backport b5d72c1 from #10401 to 2.10.

This job is useful to run, to be able to manually check the results, but
given that it fails every time and we ignore the failure in the
pipeline, there is no reason to block the entire pipeline waiting for it
to finish.

## 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)

---------

Co-authored-by: Brett Langdon <[email protected]>
Co-authored-by: Romain Komorn <[email protected]>

.gitlab/dogfood.yml

@@ -1,24 +1,7 @@
-dogfood-dogweb-failed:
-  stage: dogfood
-  tags: ["arch:amd64"]
-  needs: ["dogfood-dogweb-trigger"]
-  when: on_failure
-  script:
-    - exit 0
-
-dogfood-dogweb:
-  stage: dogfood
-  tags: ["arch:amd64"]
-  needs: ["dogfood-dogweb-trigger"]
-  when: on_success
-  script:
-    - exit 0
-
 dogfood-dogweb-trigger:
   stage: dogfood
   trigger:
     project: DataDog/dogweb
-    strategy: depend
     branch: emmett.butler/ddtrace-unstable-dogfooding
   allow_failure: true
   variables: