feat(auth): migrate Login & Register to React Hook Form + Zod (#509)

[Rufai-Ahmed]

Summary

Migrates the core auth forms from manual useState validation to React Hook Form + Zod, establishing a consistent, type-safe pattern for the rest of the app's forms (#509).

Changes

• Added react-hook-form + @hookform/resolvers.
• LoginForm and RegisterForm now use useForm + zodResolver, reusing the existing schemas in lib/validations/auth.ts (loginSchema, registerSchema) instead of hand-rolled validate()/safeParse.
• Added a LoginFormInput type so the rememberMe default is handled correctly across Zod's input/output transform (useForm<LoginFormInput, _, LoginFormData>).
• Preserved all existing behaviour and a11y: username-availability check, password-strength indicator, terms-agreement gate, social login, aria-invalid/aria-describedby, and error messaging.

Scope

The issue lists "all forms" plus analytics/perf/docs. This PR converts the two core auth forms as the canonical RHF+Zod template; the remaining forms (password reset, tournament registration, withdraw modal, contact) can adopt the same pattern in follow-ups.

Testing

tsc --noEmit is clean for LoginForm.tsx, RegisterForm.tsx, and validations/auth.ts. (The repo has unrelated pre-existing type errors in other areas.)

Closes #509

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