Load Profile state from Thread and tie visibility to the thread's model (#30090)

When deciding if a model supports tools or not, we weren't reading from
the configured model in a given thread.

This also stores the profile on the thread, which matches the behavior
of the Model and Max Mode, which we also already store per thread.

Hopefully this helps alleviate some confusion.

Release Notes:

- agent: Save profile selection per-Agent thread

crates/agent/src/thread_store.rs

@@ -657,6 +657,8 @@ pub struct SerializedThread {
     pub model: Option<SerializedLanguageModel>,
     #[serde(default)]
     pub completion_mode: Option<CompletionMode>,
+    #[serde(default)]
+    pub profile: Option<AgentProfileId>,
 }
 
 #[derive(Serialize, Deserialize, Debug)]
@@ -802,6 +804,7 @@ impl LegacySerializedThread {
             exceeded_window_error: None,
             model: None,
             completion_mode: None,
+            profile: None,
         }
     }
 }