feat(dashboard): add text search to the Experience list #1928

Feature description

Add text search to the Dashboard Experience list using the existing family-scoped Artifact search API.

Problem and proposed solution

The Methods page supports Skill search, but users can only browse Experiences.

Reuse the existing search form and Experience search semantics. Keep normal browsing when the query is empty.

Acceptance:

• Queries return matching approved, active Experiences in the selected Scope.
• Clearing the query restores browsing.
• Query state is preserved during supported navigation.
• No matches and request failures have distinct messages.
• Labels and feedback work in English and Chinese.

Add behavior coverage for search, clearing, and failure handling.

Additional context

The search backend was implemented in #1862; this task only adds Dashboard support.

Entry points:

• src/powercontext/server/dashboard/content.py
• src/powercontext/server/dashboard/templates/methods.html

Coordinate shared Dashboard changes with #1813.

This issue will be open for claiming on October 20, 2026. Please wait until then to claim it.

Are you willing to contribute to this feature?

• Yes, I am willing to contribute code, docs, or design feedback.