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/tests/common/mod.rs

@@ -1,3 +1,8 @@
+// Shared test helpers. Each integration test binary picks the subset it needs,
+// so dead-code lints on the unused helpers fire per-binary; suppress at the
+// module level.
+#![allow(dead_code)]
+
 use std::sync::Arc;
 
 use axum::body::Body;