docs(ai-chat): document HITL pause suspension and maxDuration (#3987)

## Summary

Adds a "Duration and cost while paused" section to the human-in-the-loop
page. It explains that a HITL pause (a no-execute tool waiting on
`addToolOutput`) suspends the run and frees compute, so the human's
thinking time does not count against `maxDuration` (which measures
active CPU time and excludes suspended waitpoint time, the same as
`wait.for`). Customers don't need to raise `maxDuration` or end the run
to support long human waits.

This was a recurring point of confusion: readers assumed the pause holds
the run open and burns the budget. Also updates the how-it-works
pseudocode ("Agent suspends (compute freed)") and links `wait.for` and
`maxDuration` on first mention.

Author: ericallam

docs/ai-chat/patterns/human-in-the-loop.mdx

@@ -20,7 +20,7 @@ Turn N:
   LLM streams text → calls askUser tool (no execute)
   streamText ends with tool-call in `input-available` state
   onTurnComplete fires (finishReason = "tool-calls")
-  Agent idle
+  Agent suspends (compute freed) — maxDuration does not tick while paused
 
 Frontend:
   Renders question + option buttons from tool input
@@ -36,6 +36,14 @@ Turn N+1:
 
 The AI SDK's `toUIMessageStream` automatically reuses the assistant message ID across the pause (we pass `originalMessages` internally), so `responseMessage` in the post-resume `onTurnComplete` is the **full merged message** — the original text, the completed tool call, and any follow-up content — not just the new parts.
 
+## Duration and cost while paused
+
+A pause doesn't hold compute. After the model calls a no-execute tool, the turn finishes and the run stays warm for `idleTimeoutInSeconds` (default 30s), then **suspends** and frees its compute, the same way [`wait.for`](/wait-for) does. The user's `addToolOutput` wakes it back up.
+
+Because the run is suspended while it waits, the human's thinking time is not billed and does **not** count against [`maxDuration`](/runs/max-duration). `maxDuration` measures active CPU time and excludes suspended waitpoint time, exactly like `wait.for`, so a user can take minutes, hours, or days to answer without the run hitting `maxDuration`. The only time that counts is each turn's actual compute plus the short warm window before each suspend.
+
+You don't need to raise `maxDuration` or end the run to support long human waits. How long a single suspended pause stays open is governed by the run's suspend timeout, not `maxDuration`; if a wait outlives it the run ends, and the next `addToolOutput` boots a fresh continuation that picks up the resolved tool result.
+
 ## Backend: define the tool
 
 A HITL tool has an `inputSchema` describing what the model can ask, but **no `execute` function**. When the LLM calls it, `streamText` returns control to your agent.