Add display_name to users table and propagate sender info through all handlers

[hiroshinishio]

Summary

• Rename get_user_public_email to get_user_public_info, returning a UserPublicInfo dataclass with both email and display_name
• Add display_name (required, no default) to upsert_user and create_user_request
• Add sender_display_name to BaseArgs and populate it from get_user_public_info in all three handlers (new_pr_handler, check_suite_handler, review_run_handler)
• Fix check_suite_handler and review_run_handler to call get_user_public_info for real email/display_name instead of hardcoding fake noreply emails and empty strings
• Title-case display names that are all lowercase or all uppercase (e.g. "wes nishio" -> "Wes Nishio", "HIROSHI" -> "Hiroshi")
• Type user_data as dict[str, str | None] to fix Any type propagation from response.json()
• Cross-ref comments between website and gitauto repos for the shared title-casing logic