fix: surface real API errors on registration form

[nicholas-ruest]

Summary

• Registration form was showing a generic "Registration failed" toast on every error, masking the real reason (e.g. "No solo spots remaining" HTTP 409 from the Cloud Function). Users couldn't tell the form was actually calling the backend.
• Register.tsx now parses the ApiError JSON body and shows the server's error message in the toast, falling back to the generic message only if parsing fails.
• scripts/seed-inventory.sh previously wrote singleRemaining, but the deployed Cloud Function reads soloRemaining. The two had drifted into separate Firestore fields, leaving the function-readable counter at 0 and blocking all solo registrations. Script now writes the correct field.

Context

The underlying production issue (solo counter at 0, family counter at 1) was already fixed via direct Firestore writes — soloRemaining=10, familyRemaining=17 (reconciled against 3 paid family registrations vs. ADR-026's cap of 20). This PR is just the code-side hardening so the next time something goes wrong, the error is visible instead of hidden.

Test plan

• npm run typecheck passes (already verified locally)
• npm run build succeeds
• After deploy, trigger a known-failing path (e.g. submit a tier that's sold out) and confirm the real server message appears in the toast
• Confirm the happy path (valid solo/buddy/family submission) still redirects to Stripe Checkout

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