refactor(api): share Pagination across admin/public; cover get-by-id auth

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

crates/api/src/pagination.rs

@@ -0,0 +1,23 @@
+//! Shared pagination query parameters used by both admin and public handlers.
+
+use serde::Deserialize;
+
+pub(crate) const DEFAULT_LIMIT: i64 = 50;
+pub(crate) const MAX_LIMIT: i64 = 200;
+
+/// Pagination query parameters with sane defaults and a hard cap.
+#[derive(Deserialize)]
+pub(crate) struct Pagination {
+    pub(crate) limit: Option<i64>,
+    pub(crate) offset: Option<i64>,
+}
+
+impl Pagination {
+    pub(crate) fn limit(&self) -> i64 {
+        self.limit.unwrap_or(DEFAULT_LIMIT).clamp(1, MAX_LIMIT)
+    }
+
+    pub(crate) fn offset(&self) -> i64 {
+        self.offset.unwrap_or(0).max(0)
+    }
+}