fix(nextjs): Flush in route handlers

[chargome]

closes https://linear.app/getsentry/issue/JS-783/nextjs-no-data-being-sent-from-server-side-functions
closes #17193

This will not fix this issue for prod deployments with turbopack as we do not have any build time instrumentation for route handlers there yet. In this case the current suggestion is to use:

import { after} from 'next/server';
import * as Sentry from '@sentry/nextjs';

export function GET() {
    after(() => {
        Sentry.flush();
    });
    // rest of your handler
}

[linear]

JS-783 [NextJS] No data being sent from server-side functions