[FF] use_built_in_project_templates_enabled -- Cleanup
<!-- Title suggestion: [Feature flag] Cleanup use_built_in_project_templates_enabled -->
## Summary
This issue is to cleanup the `use_built_in_project_templates_enabled` feature flag, after the feature flag has been enabled by default for an appropriate amount of time in production.
At this point, we can also remove the `experiment` label from the GraphQL argument exposed in https://gitlab.com/gitlab-org/gitlab/-/work_items/593620+
<!-- Short description of what the feature is about and link to relevant other issues. Ensure to note if the feature will be removed completely or will be productized-->
## Owners
- Team: NAME_OF_TEAM
- Most appropriate slack channel to reach out to: `#g_create_source-code`
- Best individual to reach out to: NAME
- PM: NAME
## Stakeholders
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- Name of a PM
- The Support Team
- The Delivery Team
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## Expectations
### What might happen if this goes wrong?
<!-- Any MRs that need to be rolled back? Communication that needs to happen? What are some things you can think of that could go wrong - data loss or broken pages? -->
### Cleaning up the feature flag
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- [ ] Specify in the issue description if this feature will be removed completely or will be productized as part of the Feature Flag cleanup
- [ ] Verify that external API consumers (e.g., IDE extensions, CLI tools) that may check this feature flag have been updated or can gracefully handle its removal.
- [ ] Create a merge request to remove `use_built_in_project_templates_enabled` feature flag. Ask for review and merge it.
- [ ] Remove all references to the feature flag from the codebase.
- [ ] Remove the YAML definitions for the feature from the repository.
- [ ] Create [a changelog entry](https://docs.gitlab.com/development/feature_flags/#changelog).
- [ ] Ensure that the cleanup MR has been deployed to both production and canary.
If the merge request was deployed before [the code cutoff](https://about.gitlab.com/handbook/engineering/releases/#self-managed-releases-1),
the feature can be officially announced in a release blog post.
- [ ] `/chatops run auto_deploy status <merge-commit-of-cleanup-mr>`
- [ ] Close [the feature issue](ISSUE LINK) to indicate the feature will be released in the current milestone.
- [ ] If not already done, clean up the feature flag from all environments by running these chatops command in `#production` channel: `/chatops run feature delete use_built_in_project_templates_enabled --dev --pre --staging --staging-ref --production`
- [ ] Close [the rollout issue](ISSUE LINK).
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/label ~"type::feature" ~"feature::addition"
/label ~"type::maintenance"
/label ~"type::bug"
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issue