Remove pull_request trigger from flaky-tests workflow

[lucia-sb]

What does this PR do?

Removes the pull_request trigger from .github/workflows/flaky-tests.yml that fired when .github/workflows/test-results-master.yml was changed.

Also simplifies the dry_run expression in the publish-test-results job, which previously included a github.event_name == 'pull_request' check that is no longer relevant.

Motivation

https://datadoghq.atlassian.net/browse/AI-6933

Review checklist (to be filled by reviewers)

• Feature or bugfix MUST have appropriate tests (unit, integration, e2e)
• Add qa/required if this PR needs QA validation, or qa/skip-qa if it does not. Exactly one of the two is required.
• If you need to backport this PR to another branch, you can add the backport/<branch-name> label to the PR and it will automatically open a backport PR once this one is merged

[dd-octo-sts]

Validation Report

All 21 validations passed.

Show details

Validation	Description	Status
agent-reqs	Verify check versions match the Agent requirements file	✅
ci	Validate CI configuration and code coverage settings	✅
codeowners	Validate every integration has a CODEOWNERS entry	✅
config	Validate default configuration files against spec.yaml	✅
dep	Verify dependency pins are consistent and Agent-compatible	✅
http	Validate integrations use the HTTP wrapper correctly	✅
imports	Validate check imports do not use deprecated modules	✅
integration-style	Validate check code style conventions	✅
jmx-metrics	Validate JMX metrics definition files and config	✅
labeler	Validate PR labeler config matches integration directories	✅
legacy-signature	Validate no integration uses the legacy Agent check signature	✅
license-headers	Validate Python files have proper license headers	✅
licenses	Validate third-party license attribution list	✅
metadata	Validate metadata.csv metric definitions	✅
models	Validate configuration data models match spec.yaml	✅
openmetrics	Validate OpenMetrics integrations disable the metric limit	✅
package	Validate Python package metadata and naming	✅
qa-label	Validate the pull request declares whether it needs QA for the next Agent release	✅
readmes	Validate README files have required sections	✅
saved-views	Validate saved view JSON file structure and fields	✅
version	Validate version consistency between package and changelog	✅

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