This PR implements the persistence layer for the telemetry system. It
introduces `FilePersistence` for local state management and integrates
it with `ClearcutLogger` to support "Daily Active" metric. I have
decided not to send `first_time_installation` events since we can deduce
them from `daily active` events where the `days_since_last_active` will
be `-1` for that case.
**Implementation Roadmap:**
This is the third in a series of PRs designed to implement the telemetry
system:
1. **CLI & Opt-out Mechanism
([Merged](https://github.com/ChromeDevTools/chrome-devtools-mcp/pull/757)):**
* Added `--usage-statistics` flag and transparency logging.
2. **Logger Scaffolding & Integration
([Merged](https://github.com/ChromeDevTools/chrome-devtools-mcp/pull/758)):**
* **`ClearcutLogger`**: Implemented the main logging entry point.
* **One-way Data Flow**: Integrated `logToolInvocation` and
`logServerStart` hooks into `main.ts` to capture events.
* **`ClearcutSender`**: Introduced a transport abstraction.
* **Type Definitions**: Added TypeScript definitions for the telemetry
Protocol Buffer messages.
3. **Persistence Layer (This PR):**
* **`FilePersistence`**: Implemented a local file-based state manager to
persist the `lastActive` timestamp.
* **Daily Active Logic**: Integrated persistence into `ClearcutLogger`
to automatically detect and log `daily_active` events (with
`days_since_last_active` calculation) via `logDailyActiveIfNeeded`.
4. **Watchdog Process Architecture (Next):**
* Move `ClearcutSender` execution to a dedicated watchdog process to
ensure reliable event transmission even during abrupt server shutdowns.
5. **Transport, Batching & Retries (Next):**
* Finalize `ClearcutSender` with actual HTTP transport logic, including
event batching and exponential backoff retries.
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