Refactor analysis input building

Extract the logic for building `AnalysisInput` into a new function
`build_analysis_input`. This function encapsulates the process of
collecting recordings, reading transcripts, and determining the last
recording modification time.

This change improves code organization and reusability by centralizing
the input building logic.

server/src/auth.rs

@@ -25,6 +25,12 @@ pub struct AuthenticatedUser {
     pub data_dir: PathBuf,
 }
 
+impl AuthenticatedUser {
+    pub fn is_admin(&self) -> bool {
+        self.role == "admin"
+    }
+}
+
 impl<S> FromRequestParts<S> for AuthenticatedUser
 where
     S: Send + Sync,
@@ -72,6 +78,12 @@ pub struct AuthenticatedWebUser {
     pub data_dir: PathBuf,
 }
 
+impl AuthenticatedWebUser {
+    pub fn is_admin(&self) -> bool {
+        self.role == "admin"
+    }
+}
+
 impl<S> FromRequestParts<S> for AuthenticatedWebUser
 where
     S: Send + Sync,