agent_servers: Use built-in interrupt handling for Claude sessions (#35154)

We no longer have to stop and restart the entire process. 
I left in the Start/Resume mode handling since we will likely need to
handle restarting Claude in other situations.

Release Notes:

- N/A

crates/agent_servers/Cargo.toml

@@ -29,6 +29,7 @@ itertools.workspace = true
 log.workspace = true
 paths.workspace = true
 project.workspace = true
+rand.workspace = true
 schemars.workspace = true
 serde.workspace = true
 serde_json.workspace = true