[Client] Throw TimeoutException on request timeout and cancel the request

[chr-hertel]

The default request timeout used `time()`, so it fired up to a second early, and it surfaced as a generic `RequestException` (-32603) without telling the server.

• the default timeout now runs as a deadline like `callTool(timeoutSeconds:)` => sub-second, `TimeoutException` and `notifications/cancelled`
• `TimeoutException` extends `RequestException`, so existing catchers keep working
• the init timeout stays error-based (probe fallback depends on it), but with `microtime()` resolution

Fixes chr-hertel#68
Fixes chr-hertel#69

🤖 Generated with Claude Code

[Copilot]

🟡 Changes recommended

The changelog does not disclose the public pending-request timestamp type compatibility change.

1 open finding

• Document timestamp type change in getPendingRequests as a BC break · New

What changed in this PR

Improves request-timeout precision and surfaces timeouts consistently as cancellable TimeoutExceptions.

Changes:

• Uses microsecond-resolution timestamps.
• Applies default timeouts as deadlines and sends cancellation signals.
• Updates exception inheritance, tests, documentation, and changelog.

File	Description
src/​Client.php	Applies the configured timeout as a deadline.
src/​Client/​State/​ClientState.php	Stores precise request timestamps.
src/​Client/​State/​ClientStateInterface.php	Updates the pending-request timestamp type.
src/​Client/​Transport/​HttpTransport.php	Uses precise timeout comparisons.
src/​Client/​Transport/​StdioTransport.php	Uses precise timeout comparisons.
src/​Exception/​TimeoutException.php	Makes timeouts request exceptions.
tests/​Integration/​CancellationTest.php	Tests default timeout timing and cancellation.
docs/​client/​errors.md	Documents timeout handling.
docs/​client/​transports.md	Documents timeout cancellation behavior.
CHANGELOG.md	Records the timeout fix.

🧠 Review effort: Balanced

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[Copilot]

🟡 Changes recommended

Timeout documentation contradicts existing tables and inaccurately claims modern HTTP sends cancellation notifications.

3 open findings

• Correct modern HTTP cancellation changelog wording · New
• Align timeout exception table with new behavior · New
• Clarify transport-specific cancellation signalling · New

1 resolved since last review

• Document timestamp type change in getPendingRequests as a BC break

🧠 Review effort: Balanced