Improve client-to-server logging endpoint

## Description

The `/logger` route has several issues with its API design:

1. **Payload in headers** — `level` and `message` are sent as HTTP headers rather than in the request body. Headers are meant for metadata, not payload, and this limits message size.

2. **Wrong status codes** — Missing level, missing message, and unrecognized log level all return 500 via the error middleware. These are client errors and should be 400 Bad Request.

3. **Fragile message parsing** — The message is JSON-stringified on the client, JSON-parsed on the server, then backslashes are stripped with `replaceAll("\\", "")`. Legitimate backslashes (file paths, regex patterns) get eaten. This workaround should be unnecessary with a proper JSON body.

4. **Manual level dispatch** — The if/else chain for log levels is unnecessary. Pino supports `logger[level](message)` for all valid levels.

5. **No source tagging** — Client-originated log entries are indistinguishable from server-originated ones when reading logs.

6. **Route name** — `/logger` is a noun describing the tool, not the action. `/log` is more conventional for a logging endpoint.

## Preferred Solution

### Server (`/log` route)

- Rename the route from `/logger` to `/log`
- Accept a JSON body: `{ level: string, message: string }`
- Validate `level` against the allowlist (`error`, `warn`, `info`, `debug`, `trace`) and return 400 for invalid values
- Return 400 for missing `level` or `message`
- Use Pino's method dispatch: `logger[level]({ source: "client" }, message)` instead of the if/else chain
- Tag all client log entries with `source: "client"` so they are distinguishable in server logs
- Keep `/logger` as a deprecated alias during a transition period

### Client (`ServerLoggerConnector`)

- Send level and message in the JSON request body instead of headers
- Update the endpoint URL from `/logger` to `/log`

### Request logging middleware

- Update the path filter to skip `/log` instead of `/logger`

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Start by locating the `/logger` route, `ServerLoggerConnector`, and the request-logging middleware path filter. Update the route and client to use `/log` with a JSON body, validation, client source tagging, and a deprecated alias, then verify that `/log` is excluded from request logging and invalid requests return 400.

Written by the indexing model from the issue text.