feat: record created_at/completed_at on reasoning ChatMessageParts (#24789)

Records reasoning start and end times on persisted reasoning
`ChatMessagePart`s so reasoning duration can be computed for stored
chats. Backend-only: no SSE changes and no frontend rendering ship in
this PR.

The `created_at` field on `ChatMessagePart` is extended to also be
present on `reasoning` parts (it previously appeared only on `tool-call`
and `tool-result`), and a new `completed_at` field is added for
`reasoning` parts.

### How timestamps are recorded

- `StreamPartTypeReasoningStart`: stamp `startedAt = dbtime.Now()` on
the active reasoning state.
- `StreamPartTypeReasoningEnd`: stamp `completedAt = dbtime.Now()` and
append both into parallel `[]time.Time` slices on `stepResult`.
- Persistence reads the slices in occurrence order (reasoning has no
provider-side ID) and applies them to the matching `ChatMessagePart` via
`buildAssistantPartsForPersist`. The first reasoning block's stamps go
onto the first reasoning part, and so on.
- `flushActiveState` flushes partial reasoning interrupted before
`StreamPartTypeReasoningEnd` with `startedAt` from the active state and
`completedAt = dbtime.Now()` at the interruption.

### Why two fields, not one?

Tool calls and results are point events. The frontend computes their
duration by subtracting the call's `created_at` from the result's
`created_at`. Reasoning is one assistant part that brackets a span, so
we record both endpoints on the part itself.

### Why not stamp in `PartFromContent`?

Same rationale as #24101: `PartFromContent` is called during both SSE
publishing and persistence. Stamping there would yield incorrect
persistence-time timestamps for reasoning blocks that finished much
earlier in the step. Instead we capture in the chatloop and apply during
persistence.

<details><summary>Implementation plan</summary>

- `codersdk/chats.go`: extend `CreatedAt`'s `variants` to include
`reasoning?`; add `CompletedAt *time.Time` with `variants:"reasoning?"`.
- `coderd/x/chatd/chatloop/chatloop.go`: extend `reasoningState` with
`startedAt`; extend `stepResult` and `PersistedStep` with parallel
`[]time.Time` reasoning slices; stamp on
`ReasoningStart`/`ReasoningEnd`; thread the slices through all
`PersistStep` call sites including the interrupt-safe path; record
partial reasoning in `flushActiveState`.
- `coderd/x/chatd/attachments.go`: walk reasoning parts in occurrence
order and apply `step.ReasoningStartedAt[i]` to `part.CreatedAt` and
`step.ReasoningCompletedAt[i]` to `part.CompletedAt`.

### Tests

- `codersdk/chats_test.go` round-trips `created_at` + `completed_at` on
reasoning parts and verifies omission when absent and partial
interrupted parts.
- `coderd/x/chatd/chatprompt/chatprompt_test.go` asserts
`PartFromContent(ReasoningContent{})` does NOT stamp timestamps.
- `coderd/x/chatd/chatloop/chatloop_test.go`
`TestRun_ReasoningTimestamps` drives a stream with two reasoning blocks
and verifies parallel slices, monotonicity, ordering, non-zero values,
and content-block ordering.
`TestRun_InterruptedReasoningFlushesTimestamps` cancels mid-reasoning
and verifies `flushActiveState` records a non-zero pair.
- `coderd/x/chatd/attachments_test.go` covers
`buildAssistantPartsForPersist` for normal interleaved reasoning,
partial (zero `completed_at`), and missing slices.

</details>

> Generated by Coder Agents.

Co-authored-by: Coder Agent <agent@coder.com>

coderd/apidoc/docs.go

@@ -16045,6 +16045,11 @@ const docTemplate = `{
                 "args_delta": {
                     "type": "string"
                 },
+                "completed_at": {
+                    "description": "CompletedAt is the time a reasoning part finished streaming,\nso reasoning duration can be computed as completed_at minus\ncreated_at. For interrupted reasoning, this is the\ninterruption time. Absent when reasoning timestamp data was\nnot recorded (e.g. messages persisted before this feature\nwas added).",
+                    "type": "string",
+                    "format": "date-time"
+                },
                 "content": {
                     "description": "The code content from the diff that was commented on.",
                     "type": "string"
@@ -16083,7 +16088,7 @@ const docTemplate = `{
                     "type": "boolean"
                 },
                 "created_at": {
-                    "description": "CreatedAt records when this part was produced. Present on\ntool-call and tool-result parts so the frontend can compute\ntool execution duration.",
+                    "description": "CreatedAt is the timestamp this part carries. The semantics\ndepend on the part type: for tool-call and tool-result parts\nit is the time the call was emitted or the result was\nproduced (tool duration is the result's created_at minus the\ncall's created_at); for reasoning parts it is the time\nreasoning started streaming.",
                     "type": "string",
                     "format": "date-time"
                 },

coderd/apidoc/swagger.json

@@ -14447,6 +14447,11 @@
 				"args_delta": {
 					"type": "string"
 				},
+				"completed_at": {
+					"description": "CompletedAt is the time a reasoning part finished streaming,\nso reasoning duration can be computed as completed_at minus\ncreated_at. For interrupted reasoning, this is the\ninterruption time. Absent when reasoning timestamp data was\nnot recorded (e.g. messages persisted before this feature\nwas added).",
+					"type": "string",
+					"format": "date-time"
+				},
 				"content": {
 					"description": "The code content from the diff that was commented on.",
 					"type": "string"
@@ -14485,7 +14490,7 @@
 					"type": "boolean"
 				},
 				"created_at": {
-					"description": "CreatedAt records when this part was produced. Present on\ntool-call and tool-result parts so the frontend can compute\ntool execution duration.",
+					"description": "CreatedAt is the timestamp this part carries. The semantics\ndepend on the part type: for tool-call and tool-result parts\nit is the time the call was emitted or the result was\nproduced (tool duration is the result's created_at minus the\ncall's created_at); for reasoning parts it is the time\nreasoning started streaming.",
 					"type": "string",
 					"format": "date-time"
 				},