Adds an optional `CreatedAt` timestamp to `tool-call` and `tool-result`
`ChatMessagePart` variants so the frontend can compute tool execution
duration (`result.created_at - call.created_at`).
Timestamps are recorded at the correct moments in the chatloop:
- **Tool-call**: when the model stream emits the tool call
- **Tool-result**: when tool execution completes (or is interrupted)
These are passed through `PersistedStep.PartCreatedAt` so the
persistence layer can apply accurate timestamps to stored parts.
SSE-published parts also carry `CreatedAt` for real-time display.
Old persisted messages without `created_at` deserialize to `nil` — fully
backward compatible.
<details><summary>Implementation notes (Coder Agents
generated)</summary>
### Why not stamp in `PartFromContent`?
`PartFromContent` is called both for SSE publishing (correct timing) and
during persistence (wrong timing — both tool-call and tool-result would
get the same "persistence time" timestamp, yielding ~0 duration).
Instead, timestamps are captured in the chatloop at the right moments
and carried through `PersistedStep.PartCreatedAt` as a
`map[string]time.Time` keyed by `"call:<id>"` / `"result:<id>"`.
### Interrupted tool calls
`persistInterruptedStep` also stamps `CreatedAt` on synthetic error
results for cancelled/interrupted tool calls, so partial duration is
available.
### Files changed
| File | Change |
|------|--------|
| `codersdk/chats.go` | Add `CreatedAt *time.Time` field |
| `codersdk/chats_test.go` | JSON round-trip test |
| `coderd/database/dbtime/dbtime.go` | Add `TimePtr` helper |
| `coderd/x/chatd/chatloop/chatloop.go` | Track timestamps, pass through
`PersistedStep` |
| `coderd/x/chatd/chatd.go` | Apply timestamps during persistence |
| `coderd/x/chatd/chatprompt/chatprompt_test.go` | Verify
`PartFromContent` does NOT stamp |
| `site/src/api/typesGenerated.ts` | Auto-generated |
</details>
---------
Co-authored-by: Ethan <39577870+ethanndickson@users.noreply.github.com>
