docs(js): move API-related content from Manual Setup to APIs page

[inventarSarah]

DESCRIBE YOUR PR

Added the APIs mentioned from our Next.js manual setup QS guide to the APIs page.
Removed content from Next.js manual setup QS guide we no longer need there (and have documented elsewhere).

Closes: #13289

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[inventarSarah]

@mydea I leave this pr on Draft for now in case you want to pick it up and fine-tune my API page updates -- let me know :)
(I tried to define the properties like some of the other definitions have but I was unsure how to define them for the functions I added)

[codecov]

Bundle Report

Changes will decrease total bundle size by 15 bytes (-0.0%) ⬇️. This is within the configured threshold ✅

Detailed changes

Bundle name	Size	Change
sentry-docs-server-cjs	11.14MB	-9 bytes (-0.0%) ⬇️
sentry-docs-client-array-push	9.47MB	-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	868.7kB	-0.0%
static/chunks/8165-*.js	-3 bytes	410.1kB	-0.0%
static/dgGYrki-*.js (New)	578 bytes	578 bytes	100.0% 🚀
static/dgGYrki-*.js (New)	77 bytes	77 bytes	100.0% 🚀
static/3XbmzHxbCCVy-*.js (Deleted)	-578 bytes	0 bytes	-100.0% 🗑️
static/3XbmzHxbCCVy-*.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	1.75MB	-0.0%
../instrumentation.js	-3 bytes	1.08MB	-0.0%
9523.js	-3 bytes	1.05MB	-0.0%

[coolguyzone]

I think it makes more sense to format this with line breaks similar to the example before it, just for the sake of readability, something like:

function withServerActionInstrumentation(
  serverActionName: string,
  options?: Options,
  callback: A,
): Promise<ReturnType<A>>;

[inventarSarah]

Good idea, thanks!
I've formatted all the functions I've added so they are more readable now 👍

[coolguyzone]

Added some formatting suggestions, but overall looks great!

[chargome]

Looks good but we need to make this a bit more discoverable as this is an important feature. We still need to add the link in "Next Steps" and maybe also place it somewhere else as well wdyt?

[inventarSarah]

Looks good but we need to make this a bit more discoverable as this is an important feature. We still need to add the link in "Next Steps" and maybe also place it somewhere else as well wdyt?

@chargome yes, thank you! I added the link to Next Steps in both Next.js quick start guides