Add inherited browser agent invocation

[chubes4]

Summary

• Adds a first-class browser agent task payload to browser Playground sessions, including inherited provider/model metadata and sanitized connector credential provenance.
• Packages inherited/explicit provider plugin paths into the browser runtime so agents/chat can run inside the disposable Playground session.
• Lets wpCodeboxBrowser.runRecipe() use the recipe-embedded task payload by default, so product callers do not need host-side model generation or proxy shims.

Verification

• npm run wordpress-plugin-smoke
• npm run browser-runtime-operation-smoke

Closes #435.

AI assistance

• AI assistance: Yes
• Tool(s): OpenCode (GPT-5.5)
• Used for: Implemented the browser-session inheritance primitive, updated browser runtime invocation behavior, and added targeted smoke coverage under Chris's direction.