Evaluate GitHub issue types for agentic issue triage classifications

## Related PR discussion

Follow-up from https://github.com/dotnet/sdk/pull/55244.

Review discussion:

- Suggestion to evaluate issue types: https://github.com/dotnet/sdk/pull/55244#discussion_r3599488584
- Reply noting this should be tracked as a follow-up: https://github.com/dotnet/sdk/pull/55244#discussion_r3604902198

## Background

The new agentic issue triage workflow currently applies existing repository labels for type classification, such as `Bug`, `enhancement`, `Feature Request`, `question`, `documentation`, and `Task`.

During review of the workflow, issue types came up as a possible modern alternative for broad bug/feature/task classification because they are organization-scoped rather than repository-specific, which could make cross-repository querying easier.

## Proposal

Evaluate whether `dotnet/sdk` should use GitHub issue types for the broad triage category while continuing to use labels for SDK-specific routing and special-purpose metadata.

The evaluation should cover:

- Which issue types are currently available to the `dotnet` organization.
- Whether the existing SDK type labels can be mapped cleanly to issue types.
- How to handle categories that do not appear to have direct built-in issue type equivalents, such as `question` and `documentation`.
- What permissions or organization-level configuration would be required to add or customize issue types.
- Whether the agentic triage workflow should set issue types directly, leave type labels unchanged, or use both during a transition period.

## Acceptance Criteria

- A recommendation is documented for whether `dotnet/sdk` should adopt issue types for agentic triage.
- If adoption is recommended, the mapping from current labels to issue types is documented.
- Any required organization-level setup or permissions are identified.
- The agentic triage workflow is updated only if the recommended path is actionable for this repository.

Start by reviewing the agentic issue triage workflow and the related discussion in dotnet/sdk#55244. Check the dotnet organization’s available issue types, label mappings, and required permissions. Document a recommendation, mappings, setup requirements, and whether the workflow should change; update it only if the recommendation is actionable.

Written by the indexing model from the issue text.