fix(frontend): skip the trailing-slash redirect and forward DELETE bodies in the API proxy

[klin2686]

Summary

1. Every API call from the browser was getting a 308 before it reached the proxy, because Next.js redirects paths ending in / and every path in lib/api.ts ends in one. This removes that extra round trip.
2. Deleting your own account always failed with a 422, because the proxy route dropped DELETE request bodies and DELETE /users/me/ needs the password in the body.

What changed

Frontend

• request() in lib/api.ts strips the trailing slash (before any query string) when calling /api/proxy; the proxy route already adds it back before forwarding to FastAPI.
• Requests made with NEXT_PUBLIC_API_URL set keep the slash, since they hit FastAPI directly and it has redirect_slashes=False.
• The proxy route in app/api/proxy/[...path]/route.ts now forwards the request body for DELETE, not just POST, PUT and PATCH. An empty body is still sent as no body.

Test plan

Manual

• 15 GET routes (tournament, events, members, shifts, tracks, assignments, audit log, roles, etc.) return identical status and body with and without the trailing slash, with no redirect on the new form.
• DELETE /users/me/ with a wrong password now returns 401 Current password is incorrect instead of 422 body: Field required.
• A DELETE without a body (/users/me/volunteer-experience/999999/) still returns 404 as before.

[railway-app]

This PR was not deployed automatically as @klin2686 does not have access to the Railway project.

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[vercel]

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Project	Deployment	Actions	Updated
nexus	Ready	Preview	Oct 16, 2026 6:34am UTC