[State Sync Redesign 3.13] Remove `metamask` Redux slice

Remove the monolithic `metamask` Redux slice entirely. Retain Redux for UI-local slices (`appState`, `confirm`, `history`, etc.).

## Steps

1. Remove `metamask` reducer from Redux store configuration
2. Delete `shared/types/background.ts` and `shared/types/background.spec.ts`
3. Remove `FlattenedBackgroundStateProxy` re-export from `shared/types/index.ts`
4. Migrate consumers of `FlattenedBackgroundStateProxy` to direct controller state type imports:
- `app/scripts/controllers/metametrics-controller.ts` — replace `MetaMaskState` type with `Pick` from individual controller state types (`PreferencesControllerState`, `NetworkState`, `AccountsControllerState`, etc.)
- `app/scripts/lib/rpc-method-middleware/handlers/request-accounts.ts` — replace `Pick` with `Pick` from `MetaMetricsControllerState`, `PermissionLogControllerState`, `PreferencesControllerState`
5. Remove `state.metamask` references from any remaining code
6. Retain Redux for UI-local slices (`appState`, `confirm`, `history`, etc.)
7. Update `handleStartUISync` in `app/scripts/ui.js` / `ui/index.js` to initialize `ControllerStateManager` from keyed initial state (instead of passing flat state to Redux preloaded state)
8. Update `setupInitialStore` — remove `metamask: metamaskState` from preloaded Redux state; `ControllerStateManager` owns this data now

## Files

- `shared/types/background.ts` (delete)
- `shared/types/background.spec.ts` (delete)
- `shared/types/index.ts` (remove re-export)
- `app/scripts/controllers/metametrics-controller.ts` (migrate types)
- `app/scripts/lib/rpc-method-middleware/handlers/request-accounts.ts` (migrate types)
- `ui/ducks/metamask/metamask.js` (delete)
- `ui/store/store.ts`
- `ui/index.js`
- `app/scripts/ui.js`

## Dependencies

Issues 3.10, 3.11, 3.12 (Sentry, state logs, and Storybook must be updated first)

## Context

Part of [State Sync Redesign — Epic 3: UI-controller subscriptions].

Review prerequisite issues 3.10, 3.11, and 3.12 first, then inspect ui/store/store.ts, ui/index.js, app/scripts/ui.js, and the listed controller and RPC handler files. Trace remaining state.metamask and FlattenedBackgroundStateProxy references before removing the Redux slice and background types. Done means ControllerStateManager owns keyed initial state, Redux retains only UI-local slices, and the named files and references are updated.

Written by the indexing model from the issue text.