docs: refresh public GUI story for 0.13.6

[moortekweb-art]

Summary

• refresh the README screenshots with current 0.13.6 Home, Settings, verified-result, and mobile captures
• replace the installation-specific managed screenshot with a generic embedded/managed/provider architecture graphic
• document the optional Local Studio and model-runtime boundary without exposing private infrastructure details
• update the README contract test and asset provenance note

Verification

• 1492 passed, 2 skipped with the project test environment
• node tests/frontend_token_race_test.js
• git diff --check
• README asset-link existence and private-detail sanitization checks
• SVG validation with xmllint

The screenshots were captured from the packaged GUI's built-in safe demo in a disposable workspace. No Node1 paths, tailnet names, model names, credentials, or maintainer workspace data are included.