feat(profile): add display name input wired to PATCH /auth/me

[amrtgaber]

Summary

• Adds a labeled display-name input on /profile, pre-filled from auth.displayName.
• Submit trims the value and PATCHes /auth/me; empty input clears the name (matches backend normalisation).
• After save, re-syncs auth state via checkAuth() so the navbar updates without a reload. Success/error toasts.

Closes #35. Frontend-only — the backend already supports display_name on PATCH /auth/me, the profile UI just didn't expose it.

Test plan

• Email/password user with no display name: open /profile, set a name, save → toast, navbar updates.
• Edit existing name, save → updated value persists.
• Clear the field → button label switches to "Clear display name", submitting toasts "Display name cleared." and the name disappears from navbar.
• Type only whitespace into a previously empty field → Save stays disabled.
• Backend returns 422 (e.g. paste 101+ chars before maxLength caps you, or have backend reject) → error toast surfaces the message.
• Steam OAuth user (display_name populated from Steam) sees their name pre-filled and can change it.

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