feat: persist customer product and shop favorites through the live API

Replace mall fixture favorites with customer-scoped endpoints, and send signed-out shoppers back to the page they left after sign-in.

Co-authored-by: Cursor <cursoragent@cursor.com>

openspec/changes/add-favorites/specs/frontend-mall/spec.md

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+## ADDED Requirements
+
+### Requirement: Live customer favorites
+The mall SHALL use the shared selected API adapter for product and shop favorite state. Product and store detail controls SHALL load persisted state, require customer authentication, prevent duplicate in-flight mutations, and survive reloads. The buyer-center favorites page and dashboard preview/counts SHALL render paginated live favorite results and remove targets through the API instead of reading `MOCK_FAVORITES` or mutating local-only state.
+
+#### Scenario: product favorite survives reload
+- **WHEN** a signed-in shopper favorites a product and reloads its detail page
+- **THEN** the favorite control remains selected from backend state
+
+#### Scenario: anonymous favorite requires sign-in
+- **WHEN** a signed-out shopper uses a product or store favorite control
+- **THEN** the mall sends the shopper to sign in with the current detail URL as the return destination
+
+#### Scenario: remove from buyer center
+- **WHEN** a shopper removes a product or shop from the favorites page
+- **THEN** the API state, visible list, dashboard preview, and visible count reflect the removal without fixture mutation
+
+#### Scenario: fixed adapter remains functional
+- **WHEN** the favorites domain is configured to fixed data
+- **THEN** detail controls and buyer-center favorite flows behave deterministically through the same shared client methods