Add context ID docs to browser skill

[shrey150]

Summary

• Document --context-id and --persist flags added in the latest browse CLI release
• Add context persistence section to REFERENCE.md under the open command and global flags
• Add Example 5 (persist login with context ID) to EXAMPLES.md
• Update SKILL.md navigation commands and mode comparison table

Test plan

• Verify the documented flags match the CLI behavior in @browserbasehq/browse-cli
• Confirm example commands work end-to-end with a real Browserbase context

🤖 Generated with Claude Code

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Note

Low Risk
Low risk: documentation-only updates describing new --context-id/--persist behavior; no runtime code changes.

Overview
Documents Browserbase context persistence for the browse CLI by adding guidance for --context-id and --persist under open and in the global flags section of REFERENCE.md.

Updates SKILL.md command snippets and the mode comparison table to reflect context-based session persistence, and adds a new EXAMPLES.md workflow showing how to persist and resume a logged-in session across runs.

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