test(fastify): Verify if upstream error is fixed and won't regress

[JPeer264]

closes #18418
closes JS-1260

A test that verifies that the upstream issue got fixed.

There was also one tiny config for playwright which was missed, so the wrong application was running.

[linear]

JS-1260 Fastify 5 integration: `reply.statusCode`  is always 200 in  `shouldHandleError` , making docs example unusable

[github-actions]

node-overhead report 🧳

Note: This is a synthetic benchmark with a minimal express app and does not necessarily reflect the real-world performance impact in an application.

Scenario	Requests/s	% of Baseline	Prev. Requests/s	Change %
GET Baseline	9,249	-	9,517	-3%
GET With Sentry	1,661	18%	1,769	-6%
GET With Sentry (error only)	5,918	64%	6,054	-2%
POST Baseline	1,177	-	1,195	-2%
POST With Sentry	566	48%	579	-2%
POST With Sentry (error only)	1,038	88%	1,068	-3%
MYSQL Baseline	3,256	-	3,359	-3%
MYSQL With Sentry	429	13%	450	-5%
MYSQL With Sentry (error only)	2,668	82%	2,718	-2%

View base workflow run

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[nicohrubec]

Nice, thanks for updating