refactor(arr): give arr-api its own jellyfin client

arr-daemon depends on arr-api, so a handler in arr-api can never
reach the daemon's private JellyfinClient. Move it into arr-api and
attach an instance to AppState, so a manual subtitle write can ask
for the same refresh import already does (#195).

crates/arr-api/Cargo.toml

@@ -18,6 +18,7 @@ reqwest = { workspace = true }
 serde = { workspace = true }
 serde_json = { workspace = true }
 sqlx = { workspace = true }
+thiserror = { workspace = true }
 tokio = { workspace = true }
 tracing = { workspace = true }
 utoipa = { workspace = true }