Add compact inspection proof contract

[cbusillo]

Summary

Adds a compact inspection proof contract to JetBrains inspection HTTP responses and hardens MCP output so ambiguous or contradictory inspection states do not look like clean readiness evidence.

What changed

• Adds inspection_proof and proof_failures to plugin/API verdict-bearing responses.
• Makes proof failures block GREEN inside the plugin verdict path.
• Carries current run state into /api/inspection/problems so an older clean snapshot cannot be reported green while a newer inspection run is active.
• Keeps specific UNKNOWN reasons such as timeout, stale_results, capture_incomplete, and inspection_still_running ahead of generic proof-failure messaging.
• Changes MCP inspection outputs to put verdict guidance before JSON.
• Sanitizes MCP UNKNOWN payloads by removing misleading zero-result fields, while preserving explicit include_stale=true cached diagnostics.
• Keeps verbose capture_diagnostic in raw HTTP responses, but removes it from normal MCP text output to reduce agent-context noise.

Validation

Commit hook / local validation passed:

JAVA_HOME=$(/usr/libexec/java_home -v 21) ./gradlew test :mcp-server-jvm:test --tests com.shiny.inspectionmcp.InspectionSnapshotStateTest --tests com.shiny.inspectionmcp.InspectionHandlerTest --tests com.shiny.inspectionmcp.mcpserver.McpServerTest
# BUILD SUCCESSFUL

JAVA_HOME=$(/usr/libexec/java_home -v 21) ./gradlew :test
# BUILD SUCCESSFUL

JAVA_HOME=$(/usr/libexec/java_home -v 21) ./gradlew :inspection-core:test
# BUILD SUCCESSFUL

JAVA_HOME=$(/usr/libexec/java_home -v 21) ./gradlew :mcp-server-jvm:test
# BUILD SUCCESSFUL

JAVA_HOME=$(/usr/libexec/java_home -v 21) ./gradlew buildPlugin
# BUILD SUCCESSFUL

Review Notes

A review-agent pass found real issues before this PR was opened. This branch includes fixes for them:

• /problems now includes current run state before proof/verdict calculation.
• MCP specific UNKNOWN reasons take precedence over generic inspection_proof_failed.
• include_stale=true keeps requested cached findings visible for explicit diagnostics.

Refs #113
Refs #114
Refs cbusillo/codex-skills#388