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feat(client): migrate to @inertiajs/react v3 #386

Job	Run time
JS build (Vite)	55s
JS lint & format	20s
Perf guards (Playwright)	1m 38s
JS tests (Vitest)	49s
Python lint & format	17s
File size (300-line cap)	18s
Python typecheck	18s
E2E smoke (Playwright)	2m 12s
Python tests	8m 6s
JS typecheck	50s
Package build (release dry-run)	17s
PR checks	4s
	16m 4s