feat: add profile includes management UI

- Add includes section to profile editor with drag-and-drop reordering
- Display included profiles with scope badges (Global, Project, Tool)
- Add 'Add Include' dropdown filtered by compatibility and cycle prevention
- Add remove button per include row
- Save includes together with profile form
- Add include count badges to profile list sidebar
- Add drag icon to Icon component

Implements config-profile-includes-ui tasks 1.1-4.3

openspec/changes/config-profile-includes-ui/design.md

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+## Context
+
+The config profiles backend already supports full ordered include composition:
+- `PUT /config-profiles/{id}/includes` accepts an ordered array of profile IDs
+- The API validates ownership, self-inclusion, existence, and cycles
+- `GET /config-profiles/{id}/preview` resolves includes and shows merged output
+- The frontend profile editor (`config-profiles.tsx`) already loads all profiles via `listConfigProfiles()`
+
+However, the profile editor UI currently has no includes management surface. Users can create individual profiles but cannot compose them. This design adds a drag-and-drop includes management section to the existing profile editor.
+
+## Goals / Non-Goals
+
+**Goals:**
+- Allow users to see which profiles a profile includes
+- Allow users to add, remove, and reorder includes
+- Prevent invalid includes (self, duplicates, cycles) in the UI
+- Show scope badges on included profiles for clarity
+- Display include count in the profile list sidebar
+- Save includes together with the profile form
+
+**Non-Goals:**
+- Backend changes (APIs already fully support this)
+- Drag-and-drop library dependency (use native HTML5 DnD)
+- Profile dependency graph visualization (future enhancement)
+- Validation of include compatibility at the scope level (backend handles this)
+
+## Decisions
+
+### Use Native HTML5 Drag and Drop
+**Rationale:** No additional dependency needed. The includes list is small (typically < 10 items), so native DnD is sufficient and lightweight. Libraries like react-beautiful-dnd add bundle size and complexity for this use case.
+**Alternative considered:** `@dnd-kit/core` — rejected to keep dependencies minimal.
+
+### Save Includes with Main Form
+**Rationale:** The user explicitly requested this. It's simpler UX than a separate save button and matches the mental model of "editing a profile."
+**Implementation:** On save, first update profile fields via `updateConfigProfile()`, then update includes via `updateProfileIncludes()`. If either fails, show error and don't clear dirty state.
+
+### Frontend Cycle Detection
+**Rationale:** Prevents the user from even selecting profiles that would create a cycle, providing immediate feedback instead of waiting for the API to reject it.
+**Implementation:** Build a graph from the current `profiles` array (which includes `includes` data), then traverse from each candidate profile to check if it can reach the current profile.
+
+### Scope Badge Display
+**Rationale:** Helps users understand why certain profiles are or aren't available for inclusion, and what scope each layer operates at.
+**Implementation:** Reuse existing scope badge logic from the profile list sidebar (Global, Project scoped, Tool scoped, Project + Tool scoped).
+
+### Include Count Badge in Sidebar
+**Rationale:** Quick visual indicator of which profiles are composite vs. standalone.
+**Implementation:** Add a small numeric badge next to the profile name when `profile.includes.length > 0`.
+
+## Risks / Trade-offs
+
+**[Risk]** Saving profile and includes as two separate API calls could lead to partial success (profile saved, includes not saved).
+→ **Mitigation:** Show clear error state if either call fails. The user can retry. Since includes are independent of profile content, partial failure is recoverable.
+
+**[Risk]** Large number of profiles could make the "Add Include" dropdown unwieldy.
+→ **Mitigation:** Cap the dropdown height and add scroll. Typical users have < 20 profiles.
+
+**[Risk]** Drag-and-drop reordering may feel clunky on mobile.
+→ **Mitigation:** This is primarily a desktop admin/settings interface. Mobile support is nice-to-have but not critical.
+
+## Migration Plan
+
+No migration needed — this is a pure frontend addition. Existing profiles with includes (created via API) will immediately show those includes in the UI.
+
+## Open Questions
+
+1. Should we show a preview of the resolved output (with includes applied) in real-time as includes change?
+   - *Tentative: No, keep the existing Preview button. Real-time resolution could be expensive and is not requested.*
+
+2. Should we allow including profiles from other users (shared profiles)?
+   - *Tentative: No, backend already restricts to own profiles. Keep it simple.*