feat: Serilog sink no longer initializes the SDK

[jamescrosswell]

The Serilog portion of #5245, following the design in this comment. The Sentry sink for Serilog now only configures the sink; Sentry has to be initialized separately via SentrySdk.Init, UseSentry, etc.

Part of #5245

Breaking changes

• SentrySerilogOptions no longer derives from SentryOptions. It carries only sink settings: MinimumEventLevel, MinimumBreadcrumbLevel, FormatProvider, TextFormatter, RestrictedToMinimumLevel, LevelSwitch. Anything else (Dsn, Release, SampleRate, …) belongs on the options used to initialize Sentry.
• SentrySerilogOptions.InitializeSdk is removed.
• The WriteTo.Sentry(string dsn, …) overload is removed. Serilog.Settings.Configuration users passing dsn (or any other core SDK setting) in WriteTo args will no longer bind to a Sentry sink method.
• ApplySerilogScopeToEvents() is renamed UseSerilog(), to match UseOpenTelemetry(). It returns void like its siblings and is now idempotent.

Before:

Log.Logger = new LoggerConfiguration()
    .WriteTo.Sentry(o =>
    {
        o.Dsn = "...";
        o.MinimumEventLevel = LogEventLevel.Error;
    })
    .CreateLogger();

After:

using var _ = SentrySdk.Init(o =>
{
    o.Dsn = "...";
    o.UseSerilog();
});

Log.Logger = new LoggerConfiguration()
    .WriteTo.Sentry(o => o.MinimumEventLevel = LogEventLevel.Error)
    .CreateLogger();

Notes for review

• UseSerilog() registers the processor that copies Serilog LogContext properties onto events. It has to live on the SentryOptions used for init, because it enriches every event, not only ones the sink creates. To keep that discoverable, the sink logs a one-time diagnostic warning when it's missing (only visible with Debug = true).
• The old WriteTo.Sentry(o => …) overload initialized the SDK but never registered that processor — only the dsn parameter overload did. That's why IntegrationTests.Simple snapshots gain inventory/MyTaskId tags: the test now calls UseSerilog(), and the processor is actually running.
• The sink no longer implements IDisposable. It never owned the hub, so Log.CloseAndFlush() no longer disposes the SDK; disposing the handle from SentrySdk.Init does that.
• SerilogAspNetSentrySdkTestFixture was initializing the SDK twice (once via WriteTo.Sentry(ValidDsn), then again via UseSentry); it now only initializes via UseSentry.
• ApiApprovalTests.Run.Net4_8.verified.txt can't regenerate on macOS; it was byte-identical to the DotNet10_0 snapshot before this change, so it's a copy of the regenerated one.

NLog, log4net and Microsoft.Extensions.Logging follow separately. The generic host replacement for builder.Logging.AddSentry(dsn) is tracked in #5572.

🤖 Generated with Claude Code

[codecov]

Codecov Report

❌ Patch coverage is 94.44444% with 1 line in your changes missing coverage. Please review.
⚠️ Please upload report for BASE (version7@21f45f0). Learn more about missing BASE report.

Files with missing lines	Patch %	Lines
src/Sentry.Serilog/SentrySink.cs	91.66%	0 Missing and 1 partial ⚠️

Additional details and impacted files

@@             Coverage Diff             @@
##             version7    #5573   +/-   ##
===========================================
  Coverage            ?   74.64%           
===========================================
  Files               ?      515           
  Lines               ?    18824           
  Branches            ?     3665           
===========================================
  Hits                ?    14051           
  Misses              ?     3894           
  Partials            ?      879           

☔ View full report in Codecov by Harness.
📢 Have feedback on the report? Share it here.

🚀 New features to boost your workflow:

• ❄️ Test Analytics: Detect flaky tests, report on failures, and find test suite problems.