feat: nest API under /api/v1, structured error envelope, paged lists

Move every handler from /api/* to /api/v1/*. /api/* is now reserved for
future versioning.

Standardise the error response shape across the API as
{"error": {"code": "snake_case", "message": "..."}}. AppError gains a
`code()` whose top-level variants are matched exhaustively without a
wildcard — new variants are a compile error until coded. 500-class
responses always emit the fixed "internal error" string and log the
real cause via tracing only.

Lock in the list pagination envelope as {"items": [...], "page": {
"limit", "offset", "total"}} and apply it to GET /api/v1/mangas. `total`
serialises as null until feat/list-search-polish lands an indexed count.

The frontend client parses the envelope into ApiError.code with an
http_error fallback for non-JSON bodies. listMangas now returns the
paged shape; the root route consumes .items. New client.test.ts covers
envelope parsing and the fallback paths.

Lockstep version bump to 0.2.0.

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

backend/src/api/pagination.rs

@@ -0,0 +1,30 @@
+//! Shared pagination envelope for list endpoints.
+//!
+//! `total` is `Option<i64>` and is always serialised — `null` when the
+//! handler hasn't computed it yet, a number once it has. The shape is fixed
+//! across `/mangas`, `/chapters`, `/bookmarks`, etc. so consumers can
+//! handle pagination uniformly.
+
+use serde::Serialize;
+
+#[derive(Debug, Serialize)]
+pub struct PageInfo {
+    pub limit: i64,
+    pub offset: i64,
+    pub total: Option<i64>,
+}
+
+#[derive(Debug, Serialize)]
+pub struct PagedResponse<T> {
+    pub items: Vec<T>,
+    pub page: PageInfo,
+}
+
+impl<T> PagedResponse<T> {
+    pub fn new(items: Vec<T>, limit: i64, offset: i64) -> Self {
+        Self {
+            items,
+            page: PageInfo { limit, offset, total: None },
+        }
+    }
+}