Capture server-side errors

[nicohrubec]

Server-side errors thrown in server routes are not captured.

Solution Brainstorm: To instrument this we can use the Server Entry Point, responsible for handling all SSR-related work as well as for handling server routes and server function requests. Tanstack users can define custom server entry points using createServerEntry (available from Tanstack Start v1.136.0), which receives a requestHandler. We can either wrap the requestHandler or createServerEntry directly. We should also take care of only reporting unexpected errors (5xx).

Tests:

• Add test that verifies that server router errors are being captured.
• Add test that expected errors are not reported.

Documentation: Need to update public and onboarding docs when this works.

Draft PR

[linear]

JS-1192

[github-actions]

A PR closing this issue has just been released 🚀

This issue was referenced by PR #19330, which was included in the 10.40.0 release.