Refactor: Use doctate-common for shared logic

Moves shared types and utility functions to a new `doctate-common`
crate.
This includes:
- API key header constant
- AckResponse and AckStatus types
- Timestamp formatting and parsing utilities

This change centralizes common functionality, reducing duplication and
improving maintainability.
The `server` crate now depends on `doctate-common`.

server/src/models.rs

@@ -1,15 +1 @@
-use serde::Serialize;
-
-#[derive(Serialize)]
-pub struct AckResponse {
-    pub case_id: String,
-    pub recorded_at: String,
-    pub status: AckStatus,
-}
-
-#[derive(Serialize)]
-#[serde(rename_all = "lowercase")]
-pub enum AckStatus {
-    Received,
-    Gone,
-}
+pub use doctate_common::ack::{AckResponse, AckStatus};