Revert "Load Profile state from Thread and tie visibility to the thread's model" (#30413)

This reverts commit 3615d6d96c.

Ultimately, we want to restore the ability to store a profile
per-thread, but for now reverting this fixes a fairly disruptive bug.

Release Notes:

- Fixed a bug causing the agent to use the wrong profile in some cases.

crates/agent/src/thread_store.rs

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