docs(dotnet): stable Metrics APIs

[Flash0ver]

DESCRIBE YOUR PR

With the next release of the Sentry .NET SDK - expected to be v6.3.0 - the Metrics APIs are no longer Experimental.
This changeset updates the respective C# code snippets.

Related PRs:

• ref!: remove Experimental from Metrics API sentry-dotnet#5023
• docs(dotnet): stable Metrics APIs sentry#110636

IS YOUR CHANGE URGENT?

Help us prioritize incoming PRs by letting us know when the change needs to go live.

• Urgent deadline (GA date, etc.):
• Other deadline: Release of the Sentry .NET SDK v6.3.0
• None: Not urgent, can wait up to 1 week+

SLA

• Teamwork makes the dream work, so please add a reviewer to your PRs.
• Please give the docs team up to 1 week to review your PR unless you've added an urgent due date to it.
  Thanks in advance for your help!

PRE-MERGE CHECKLIST

Make sure you've checked the following before merging your changes:

• Checked Vercel preview for correctness, including links
• PR was reviewed and approved by any necessary SMEs (subject matter experts)
  • @jamescrosswell
• PR was reviewed and approved by a member of the Sentry docs team

EXTRA RESOURCES

• Sentry Docs contributor guide

[vercel]

The latest updates on your projects. Learn more about Vercel for GitHub.

Project	Deployment	Actions	Updated (UTC)
sentry-docs	Ready	Preview, Comment	Mar 13, 2026 2:37pm

1 Skipped Deployment

Project	Deployment	Actions	Updated (UTC)
develop-docs	Ignored		Mar 13, 2026 2:37pm