feat(tanstackstart-react): Auto-copy build file to correct folder

[nicohrubec]

WIP

Closes #18665

[github-actions]

Codecov Results 📊

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[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	8,748	-	9,199	-5%
GET With Sentry	1,659	19%	1,746	-5%
GET With Sentry (error only)	6,034	69%	6,154	-2%
POST Baseline	1,193	-	1,177	+1%
POST With Sentry	588	49%	583	+1%
POST With Sentry (error only)	1,040	87%	1,054	-1%
MYSQL Baseline	3,250	-	3,323	-2%
MYSQL With Sentry	426	13%	450	-5%
MYSQL With Sentry (error only)	2,647	81%	2,685	-1%

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