refactor: update remaining modules to use plugin-identity constants

Update various modules to use centralized constants from plugin-identity:
- get-local-version/formatter: Use PUBLISHED_PACKAGE_NAME
- run/session-resolver: Use PUBLISHED_PACKAGE_NAME
- background-agent/task-poller: Use PUBLISHED_PACKAGE_NAME
- mcp-oauth/provider: Use PUBLISHED_PACKAGE_NAME
- auto-update-checker/constants: Use ACCEPTED_PACKAGE_NAMES
- comment-checker/downloader: Use PUBLISHED_PACKAGE_NAME
- legacy-plugin-toast/hook: Use PLUGIN_NAME
- shared/data-path: Use CACHE_DIR_NAME
- shared/external-plugin-detector: Use ACCEPTED_PACKAGE_NAMES
- shared/logger: Use LOG_FILENAME
- tools/ast-grep/downloader: Use PUBLISHED_PACKAGE_NAME
- tools/call-omo-agent/tools: Use PUBLISHED_PACKAGE_NAME
- tools/delegate-task/category-resolver: Use PUBLISHED_PACKAGE_NAME
- tools/grep/constants: Use PUBLISHED_PACKAGE_NAME
- tools/grep/downloader: Use PUBLISHED_PACKAGE_NAME
- tools/lsp/lsp-client-wrapper: Use PUBLISHED_PACKAGE_NAME

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