chatCustomizations: support grouping and badges for external provider items (#305813)

* feat: enhance AICustomizationListWidget with grouping and badge support for external customization items

* feat: add user data profile service and infer storage from URI in AICustomizationListWidget

* Copilot CLI session 8af2fd4a-10fe-4bba-b408-f1b90cebc8dc changes

* docs: add chatSessionCustomizationProvider API chain to customizations editor skill

Co-authored-by: Copilot <[email protected]>

* fix: address PR review feedback

- Remove duplicate sectionToIcon, reuse getSectionIcon instance method
- Use Map for O(1) groupKey lookups instead of O(n²) includes/find
- Check active project root in inferStorageFromUri for Sessions window
- Set pluginUri on provider items and use it for storage inference
- Remove redundant plugin check from inferStorageFromUri (handled by caller)

Co-authored-by: Copilot <[email protected]>

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Co-authored-by: Copilot <[email protected]>