docs(dotnet/logs): add Serilog integration and update Logger APIs

[Flash0ver]

DESCRIBE YOUR PR

Follow-up to #14583.
Updates the docs of Structured Logs for the .NET SDK for Release 5.15.0:

• feat(logs): rework method overloads of Structured Logger sentry-dotnet#4451
• feat: add Serilog integration sentry-dotnet#4462

Should be merged shortly after the Release of the new Package version.

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 Sentry .NET SDK v5.15.0
• 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)
• PR was reviewed and approved by a member of the Sentry docs team

EXTRA RESOURCES

• Sentry Docs contributor guide

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Project	Deployment	Preview	Comments	Updated (UTC)
sentry-docs	Ready	Preview	Comment	Aug 25, 2025 4:46pm

1 Skipped Deployment

Project	Deployment	Preview	Comments	Updated (UTC)
develop-docs	Ignored	Preview		Aug 25, 2025 4:46pm

[codecov]

Bundle Report

Changes will increase total bundle size by 7.44kB (0.03%) ⬆️. This is within the configured threshold ✅

Detailed changes

Bundle name	Size	Change
sentry-docs-client-array-push	9.9MB	-6 bytes (-0.0%) ⬇️
sentry-docs-server-cjs	12.47MB	7.45kB (0.06%) ⬆️

Affected Assets, Files, and Routes:

view changes for bundle: sentry-docs-server-cjs

Assets Changed:

Asset Name	Size Change	Total Size	Change (%)
1729.js	-3 bytes	1.78MB	-0.0%
../instrumentation.js	-3 bytes	1.1MB	-0.0%
9523.js	-3 bytes	1.08MB	-0.0%
../app/[[...path]]/page.js.nft.json	2.48kB	760.93kB	0.33%
../app/platform-redirect/page.js.nft.json	2.48kB	760.85kB	0.33%
../app/sitemap.xml/route.js.nft.json	2.48kB	758.32kB	0.33%

view changes for bundle: sentry-docs-client-array-push

Assets Changed:

Asset Name	Size Change	Total Size	Change (%)
static/chunks/pages/_app-*.js	-3 bytes	882.71kB	-0.0%
static/chunks/8321-*.js	-3 bytes	425.87kB	-0.0%
server/middleware-*.js	-5.55kB	1.0kB	-84.74%
server/middleware-*.js	5.55kB	6.55kB	555.3% ⚠️
static/VN_5x3do0_-*.js (New)	684 bytes	684 bytes	100.0% 🚀
static/VN_5x3do0_-*.js (New)	77 bytes	77 bytes	100.0% 🚀
static/1OKzuFBTmLVwKpBNdChN8/_buildManifest.js (Deleted)	-684 bytes	0 bytes	-100.0% 🗑️
static/1OKzuFBTmLVwKpBNdChN8/_ssgManifest.js (Deleted)	-77 bytes	0 bytes	-100.0% 🗑️

[jamescrosswell]

LGTM

[coolguyzone]

LGTM