Ensure web adapter session IDs survive duplicated tabs

[schickling]

Summary

• gate the persisted session id behind a Web Locks rendezvous so duplicate tabs mint a fresh id before starting the leader worker
• add a Playwright regression that boots two tabs with a cloned sessionStorage snapshot and asserts the second tab re-keys itself
• document the Web Locks requirement and how to opt into a shared session id via adapter options
• explain in code comments why the session-id lock acquisition loops, re-mints candidates when another tab holds the lock, and link back to the duplicated-tab spec in issue Client document state isn't properly isolated when using browser "Duplicate tab" feature #377 for future reference

Testing

• direnv exec . mono lint --fix

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https://chatgpt.com/codex/tasks/task_e_68d02dad79048329a2efe66623096637