[`MetamaskController` B.5] Complete `ProviderEngineFactory` extraction

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**Sub-epic:** [#41737 — `MetamaskController` decomposition: extension-specific modules](https://github.com/MetaMask/metamask-extension/issues/41737)
**Files:**
- `app/scripts/lib/provider-engine/index.ts` (new)
- `app/scripts/lib/provider-engine/provider-engine.test.ts` (new)
- `app/scripts/metamask-controller.js`

**Size:** L

## Problem

Provider-engine construction lives inline on `MetamaskController` across three method bodies: `setupProviderEngineEip1193`, `setupProviderEngineCaip`, and `setupCommonMiddlewareHooks`. Extract them into a single `ProviderEngineFactory` under `provider-engine/` so the middleware stack is independently constructible, testable, and consumable by `connection-manager` (B.2) via dependency injection.

An earlier exploration sketched the factory shape (`ProviderEngineDependencies` type and method signatures) in [commit `1329be94ef`](https://github.com/MetaMask/metamask-extension/commit/1329be94ef); use it as an implementation hint when shaping the new module, but the extraction itself starts from the current `MetamaskController` method bodies on `main`.

## Solution

1. Create `app/scripts/lib/provider-engine/` with `index.ts` exporting `ProviderEngineFactory` and a `ProviderEngineDependencies` type.
2. Port each of the three method bodies into the factory, preserving middleware ordering.
3. Rewrite `this.fooController.bar(...)` as `messenger.call(...)` where an action exists; remaining references become typed fields on `ProviderEngineDependencies`.
4. Update `MetamaskController`'s call sites to delegate to the factory.
5. Delete the three method definitions from `metamask-controller.js`.
6. If `index.ts` becomes unwieldy during the port (~900+ lines), split into `eip1193.ts` / `caip.ts` / `common-hooks.ts`.
7. Add unit tests for middleware composition.

## Acceptance criteria

- [ ] `app/scripts/lib/provider-engine/index.ts` exists with `buildEip1193Engine` and `buildCaipEngine` fully bodied (not throwing)
- [ ] `MetamaskController`'s `setupProviderEngineEip1193`, `setupProviderEngineCaip`, and `setupCommonMiddlewareHooks` definitions deleted; call sites delegate to the factory
- [ ] `connection-manager` (B.2) consumes the factory via injected dep, not via a `MetamaskController` method reference
- [ ] `yarn test` green, `tsc` green, extension dev build boots

## Dependencies

**B.2** — needs `ConnectionManager` caller interface stable.

Start with the three provider-engine methods in app/scripts/metamask-controller.js and review commit 1329be94ef for the proposed factory shape. Create and test app/scripts/lib/provider-engine/index.ts, preserving middleware ordering, then update the controller call sites and remove the old definitions. Run the provider-engine tests, yarn test, tsc, and the extension dev build to verify completion.

Written by the indexing model from the issue text.