Add Serilog console logging across the API

Information at endpoint and service-method boundaries, Debug in deeper
helpers, Warning before expected/recoverable failures (not-found,
validation, agent tool errors), Error on caught exceptions. Serilog
wraps the exception handler so request-completion logs report the
resolved status code rather than the raw exception. Never logs prose
bodies or the Anthropic API key.

tests/Novelly.Api.Tests/CapturingLogger.cs

@@ -0,0 +1,24 @@
+using Microsoft.Extensions.Logging;
+
+namespace Novelly.Api.Tests;
+
+/// <summary>Records every entry logged through it, so tests can assert on what a service logged.</summary>
+public record CapturedLogEntry(LogLevel Level, string Message, Exception? Exception);
+
+/// <summary>
+/// A test double for <see cref="ILogger{TCategoryName}"/> that captures entries instead of
+/// writing them anywhere, so tests can assert a service logged at the right level with the
+/// right values without standing up a real sink.
+/// </summary>
+public class CapturingLogger<T> : ILogger<T>
+{
+    public List<CapturedLogEntry> Entries { get; } = [];
+
+    public IDisposable? BeginScope<TState>(TState state) where TState : notnull => null;
+
+    public bool IsEnabled(LogLevel logLevel) => true;
+
+    public void Log<TState>(
+        LogLevel logLevel, EventId eventId, TState state, Exception? exception, Func<TState, Exception?, string> formatter) =>
+        Entries.Add(new CapturedLogEntry(logLevel, formatter(state, exception), exception));
+}