feat: continuous reader mode with persisted preference

Add a vertical-scroll continuous mode to the reader alongside the
existing single-page mode. A segmented toggle in the reader top bar
switches between them; in continuous mode a gap selector
(None/Small/Medium/Large → 0/12/32/64px) controls the spacing
between stacked pages. Settings page mirrors the same controls.

Backend: new user_preferences table (one row per user, lazily
inserted, ON DELETE CASCADE) and GET/PATCH /api/v1/auth/me/preferences
gated by the existing CurrentUser extractor. Allowed values are
enforced both by API validation and table-level CHECK constraints.
Eight integration tests cover defaults, persistence, partial
updates, validation errors, auth, per-user isolation, and cascade.

Frontend: a new preferences store mirrors the theme-store pattern
with a localStorage shadow so anonymous browsers get a consistent
experience and logged-in users don't flash defaults while the
server response is in flight. Server values that the frontend
doesn't recognize (forward-compat) are ignored rather than poisoning
the UI; non-401 PATCH errors revert the optimistic local update;
logout clears the shadow so user A's settings don't follow user B
on a shared browser.

In continuous mode native scrolling handles Space/PageDown/arrows;
Home/End remain wired and call scrollIntoView() so jumping to chapter
bounds stays one keystroke. Single-page mode (chevrons, arrow-key
pagination, next-page preload) is unchanged.

Versions bumped 0.13.0 → 0.14.0 in lockstep.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

backend/src/repo/mod.rs

@@ -5,3 +5,4 @@ pub mod manga;
 pub mod page;
 pub mod session;
 pub mod user;
+pub mod user_preferences;

backend/src/repo/user_preferences.rs

@@ -0,0 +1,48 @@
+//! Per-user reader preferences. Rows are lazily inserted on the first
+//! upsert — a user that has never customised their settings has no row,
+//! and reads fall back to the in-memory defaults in `UserPreferences::defaults_for`.
+
+use sqlx::PgPool;
+use uuid::Uuid;
+
+use crate::domain::UserPreferences;
+use crate::error::AppResult;
+
+pub async fn find(pool: &PgPool, user_id: Uuid) -> AppResult<Option<UserPreferences>> {
+    let row = sqlx::query_as::<_, UserPreferences>(
+        r#"
+        SELECT user_id, reader_mode, reader_page_gap, updated_at
+        FROM user_preferences
+        WHERE user_id = $1
+        "#,
+    )
+    .bind(user_id)
+    .fetch_optional(pool)
+    .await?;
+    Ok(row)
+}
+
+pub async fn upsert(
+    pool: &PgPool,
+    user_id: Uuid,
+    reader_mode: &str,
+    reader_page_gap: &str,
+) -> AppResult<UserPreferences> {
+    let row = sqlx::query_as::<_, UserPreferences>(
+        r#"
+        INSERT INTO user_preferences (user_id, reader_mode, reader_page_gap)
+        VALUES ($1, $2, $3)
+        ON CONFLICT (user_id) DO UPDATE
+            SET reader_mode = EXCLUDED.reader_mode,
+                reader_page_gap = EXCLUDED.reader_page_gap,
+                updated_at = now()
+        RETURNING user_id, reader_mode, reader_page_gap, updated_at
+        "#,
+    )
+    .bind(user_id)
+    .bind(reader_mode)
+    .bind(reader_page_gap)
+    .fetch_one(pool)
+    .await?;
+    Ok(row)
+}