docs(js): Review and update Fastify quick start guide

[inventarSarah]

DESCRIBE YOUR PR

Updated the Fastify quick start guide to be consistent with our other quick start guides.

I want to merge #14218 first, as this branch contains changes that are also needed for the changes in this pr

Closes #14246

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  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

[vercel]

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Name	Status	Preview	Comments	Updated (UTC)
sentry-docs	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Jul 3, 2025 7:45am

1 Skipped Deployment

Name	Status	Preview	Comments	Updated (UTC)
develop-docs	⬜️ Ignored (Inspect)			Jul 3, 2025 7:45am

[codecov]

Bundle Report

Changes will increase total bundle size by 960 bytes (0.0%) ⬆️. This is within the configured threshold ✅

Detailed changes

Bundle name	Size	Change
sentry-docs-server-cjs	11.8MB	966 bytes (0.01%) ⬆️
sentry-docs-client-array-push	9.8MB	-6 bytes (-0.0%) ⬇️

Affected Assets, Files, and Routes:

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	873.24kB	-0.0%
static/chunks/7750-*.js	-3 bytes	415.85kB	-0.0%
server/middleware-*.js	5.55kB	6.55kB	555.3% ⚠️
server/middleware-*.js	-5.55kB	1.0kB	-84.74%
static/eiqx0AZnp7Iy0AvA8coTP/_buildManifest.js (New)	684 bytes	684 bytes	100.0% 🚀
static/eiqx0AZnp7Iy0AvA8coTP/_ssgManifest.js (New)	77 bytes	77 bytes	100.0% 🚀
static/LCYIWwdRDD_44Jh-*.js (Deleted)	-684 bytes	0 bytes	-100.0% 🗑️
static/LCYIWwdRDD_44Jh-*.js (Deleted)	-77 bytes	0 bytes	-100.0% 🗑️

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

Assets Changed:

Asset Name	Size Change	Total Size	Change (%)
1729.js	-3 bytes	1.64MB	-0.0%
../instrumentation.js	-3 bytes	973.36kB	-0.0%
9523.js	-3 bytes	949.31kB	-0.0%
../app/[[...path]]/page.js.nft.json	325 bytes	692.72kB	0.05%
../app/platform-redirect/page.js.nft.json	325 bytes	692.63kB	0.05%
../app/sitemap.xml/route.js.nft.json	325 bytes	690.6kB	0.05%