Update RN Custom Metrics to use Sentry.setMeasurement

[krystofwoldrich]

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Fixes getsentry/sentry-react-native#4488

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PRE-MERGE CHECKLIST

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• Checked Vercel preview for correctness, including links
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• PR was reviewed and approved by a member of the Sentry docs team

LEGAL BOILERPLATE

Look, I get it. The entity doing business as "Sentry" was incorporated in the State of Delaware in 2015 as Functional Software, Inc. and is gonna need some rights from me in order to utilize my contributions in this here PR. So here's the deal: I retain all rights, title and interest in and to my contributions, and by keeping this boilerplate intact I confirm that Sentry can use, modify, copy, and redistribute my contributions, under Sentry's choice of terms.

EXTRA RESOURCES

• Sentry Docs contributor guide

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Name	Status	Preview	Comments	Updated (UTC)
sentry-docs	✅ Ready (Inspect)	Visit Preview	💬 Add feedback	Feb 3, 2025 9:55pm

2 Skipped Deployments

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[recurser]

I reported the origin issue - confirming that this fixes it 👍 Thanks!

[krystofwoldrich]

@recurser Thank you for the confirmation.

[coolguyzone]

Looks good, thanks!

[codecov]

Bundle Report

Changes will increase total bundle size by 1.06kB (0.01%) ⬆️. This is within the configured threshold ✅

Detailed changes

Bundle name	Size	Change
sentry-docs-server-cjs	10.63MB	1.07kB (0.01%) ⬆️
sentry-docs-client-array-push	9.31MB	-6 bytes (-0.0%) ⬇️

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	1.63MB	-0.0%
../instrumentation.js	-3 bytes	965.23kB	-0.0%
9523.js	-3 bytes	941.45kB	-0.0%
../app/[[...path]]/page.js.nft.json	359 bytes	374.34kB	0.1%
../app/platform-redirect/page.js.nft.json	359 bytes	374.25kB	0.1%
../app/sitemap.xml/route.js.nft.json	359 bytes	372.22kB	0.1%

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	866.04kB	-0.0%
static/chunks/9557-*.js	-3 bytes	391.11kB	-0.0%
server/middleware-*.js	5.55kB	6.55kB	555.3% ⚠️
server/middleware-*.js	-5.55kB	1.0kB	-84.74%
static/mGHYYfup02rZr-*.js (New)	578 bytes	578 bytes	100.0% 🚀
static/mGHYYfup02rZr-*.js (New)	77 bytes	77 bytes	100.0% 🚀
static/l80_Bm3Ieee2gGuZzW-*.js (Deleted)	-77 bytes	0 bytes	-100.0% 🗑️
static/l80_Bm3Ieee2gGuZzW-*.js (Deleted)	-578 bytes	0 bytes	-100.0% 🗑️