Add start_date in the Issue REST API
<!-- This issue template can be used as a great starting point for feature requests. Learn more about the process: https://handbook.gitlab.com/handbook/product/product-management/#customer-feature-requests. The section "Release notes" can be used as a summary of the feature and is also required if you want to have your release post blog MR auto generated using the release post item generator: https://about.gitlab.com/handbook/marketing/blog/release-posts/#release-post-item-generator. The remaining sections are the backbone for every feature in GitLab.
The goal of this template is brevity for quick/smaller iterations. For a more thorough list of considerations for larger features or feature sets, you can leverage the detailed [feature proposal](https://gitlab.com/gitlab-org/gitlab/-/blob/master/.gitlab/issue_templates/Feature%20proposal%20-%20detailed.md). -->
### Release notes
<!-- What is the problem and solution you're proposing? This content sets the overall vision for the feature and serves as the release notes that will populate in various places, including the [release post blog](https://about.gitlab.com/releases/categories/releases/) and [Gitlab project releases](https://gitlab.com/gitlab-org/gitlab/-/releases). " -->
### Problem to solve
With the [New Issue look](https://about.gitlab.com/releases/2025/04/17/gitlab-17-11-released/#new-issue-look-now-generally-available), users are also able to set the `Start Date` of an issue in the UI. This is currently being populated using the [GraphQL API endpoint](https://docs.gitlab.com/api/graphql/reference/#workitemwidgetstartandduedateupdateinput) and is not yet supported by the [REST API endpoint](https://docs.gitlab.com/api/issues/#new-issue).
### Proposal
Add support for the `Start Date` by adding a corresponding `start_date` parameter in the REST API endpoint.
### Intended users
* [Parker (Product Manager)](https://handbook.gitlab.com/handbook/product/personas/#parker-product-manager)
* [Delaney (Development Team Lead)](https://handbook.gitlab.com/handbook/product/personas/#delaney-development-team-lead)
* [Presley (Product Designer)](https://handbook.gitlab.com/handbook/product/personas/#presley-product-designer)
* [Sasha (Software Developer)](https://handbook.gitlab.com/handbook/product/personas/#sasha-software-developer)
### Feature Usage Metrics
<!-- How are you going to track usage of this feature? Think about user behavior and their interaction with the product. What indicates someone is getting value from it?
Explore (../../doc/development/internal_analytics/internal_event_instrumentation/quick_start.md) for a guide.
-->
### Does this feature require an audit event?
<!--- Checkout these docs to know more
https://docs.gitlab.com/ee/development/audit_event_guide/#what-are-audit-events
https://docs.gitlab.com/administration/compliance/audit_event_reports/
--->
<!-- Label reminders
Make sure to add the appropriate labels for the product stage and/or group (e.g ~"devops::plan") if known and add a comment tagging the appropriate Product Manager.
Use the following resources to find the appropriate labels:
- Use only one tier label choosing the lowest tier this is intended for
- https://gitlab.com/gitlab-org/gitlab/-/labels
- https://about.gitlab.com/handbook/product/categories/features/
Examples:
/label ~group:: ~section:: ~Category:
/label ~"GitLab Free" ~"GitLab Premium" ~"GitLab Ultimate"
-->
issue