Compute ContextBudget on demand from typed sources

Remove cached context_budget field and measure_budget(). Budget
is computed on demand via budget() which calls
ContextState::budget(). Each bucket counted from its typed source.
Memory split from conversation by identifying memory tool calls.

Co-Authored-By: Proof of Concept <poc@bcachefs.org>

src/bin/poc-agent.rs

@@ -964,7 +964,7 @@ async fn run(cli: cli::CliArgs) -> Result<()> {
             completion_tokens: 0,
             model: agent_guard.model().to_string(),
             turn_tools: 0,
-            context_budget: agent_guard.context_budget.status_string(),
+            context_budget: agent_guard.budget().status_string(),
         }));
     }