[product-manager-impersonator] Failure-cause labels for agent incident issues

## Feature Idea

**Summary:** Automatically classify and label agent-generated failure issues by root failure cause so maintainers can triage faster.

## Why a Customer Would Want This
Maintainers running scheduled workflows see multiple failure issues over time, but today they often have the same broad categorization. Cause-specific labels (for example auth/config/rate-limit/runtime) let teams route incidents immediately, create saved searches, and separate transient platform noise from repository misconfiguration.

## Rough Implementation Sketch
- Add a small failure-classification map in failure-issue reporting paths used by scheduled workflows.
- Apply one or more standardized labels based on known failure signatures at issue creation time.
- Reuse the existing maintenance label bootstrap path so missing labels can be created automatically.
- Document the label meanings and a couple of saved-search examples in workflow docs.

## Why It Won't Be That Hard
The repository already supports failure issue reporting and already includes label-creation plumbing in maintenance flows. This is a narrow addition: classify known failure patterns and attach labels using existing issue/label pathways.

## Evidence
- Failure issue reporting is already configurable in `.github/workflows/gh-aw-product-manager-impersonator.md` (inputs `report-failure-as-issue`, lines 64-68).
- Maintenance workflow already supports label bootstrapping via `create_labels` in `.github/workflows/agentics-maintenance.yml` (operation options around lines 43-56, and job step around lines 343-353).
- Label bootstrap is documented for maintainers in `docs/workflows/gh-agent-workflows.md` (manual `create_labels` operation, lines 146-149).
- Recent open/closed failure issues with similar broad categorization indicate recurring triage demand (examples from `/tmp/previous-findings.json`: #1649, #1573, #1492).

## Duplicate Check
This is distinct from existing ideas focused on whether to report failures (`#864`) or replay behavior (`#893`): this proposal targets **automatic failure-cause classification and routing labels** on the issues that are already being filed.

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[What is this?](https://ela.st/github-ai-tools) | [From workflow: Trigger Product Manager Impersonator](https://github.com/elastic/ai-github-actions/actions/runs/30535650093)

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Start with .github/workflows/gh-aw-product-manager-impersonator.md around report-failure-as-issue, then inspect create_labels in .github/workflows/agentics-maintenance.yml and its documentation in docs/workflows/gh-agent-workflows.md. Map the known failure signatures to standardized labels, reuse the existing bootstrap path, and document label meanings and saved-search examples.

Written by the indexing model from the issue text.