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/Cargo.toml

@@ -5,6 +5,7 @@ edition.workspace = true
 default-run = "doctate-server"
 
 [dependencies]
+doctate-common = { path = "../doctate-common" }
 axum = { version = "0.8", features = ["multipart"] }
 tokio.workspace = true
 reqwest.workspace = true