refactor: remove legacy live-read and injected-history chat context paths (#26585)

This PR makes the agent-pushed pinned snapshot
(`chat_context_resources`) the sole source of workspace context for
chats, completing the "Release 5" cleanup. It removes legacy mechanisms
now superseded by the snapshot that agents push over dRPC
(`PushContextState`) and refresh via `chat-context/refresh`.

Removed:

- **Live-read at turn time.** MCP tool discovery, skill live-body reads,
and the instruction/skill history fallback that dialed the workspace on
every turn.
- **Context injected as message history.** The
`persist_workspace_context` generation action and its decision-loop
guard.
- **The legacy write path.** `POST`/`DELETE
/api/v2/workspaceagents/me/experimental/chat-context`, the agentsdk
`AddChatContext`/`ClearChatContext` methods, and the CLI one-shot
writer.
- **The `chats.last_injected_context` column** and all of its plumbing
(migration `000529`, queries, `db2sdk`, `dbauthz`, audit table, and the
frontend `ContextUsageIndicator` fallback).

Subagent context inheritance no longer copies parent context messages;
children now hydrate the parent's pinned `chat_context_resources` on
create, which yields an identical pin for the same workspace and agent.

What stays (still served by the live agent connection, not the
snapshot): `read_skill_file` supporting-file reads, `read_skill`
supporting-file listing, and MCP tool execution.

> [!NOTE]
> Migration `000529` drops `chats.last_injected_context` and recreates
the `chats_expanded` view without it. The down migration restores both.

<details>
<summary>Decision log (D1-D5)</summary>

- **D1 (subagent inheritance):** Re-point inheritance from the legacy
message copy to a pinned hydrate. Children call
`hydrateChatContextOnCreate` instead of copying parent context messages.
- **D2 (`persist_workspace_context`):** Remove the generation action
entirely along with the decision-loop guard it existed to satisfy, since
context is never injected into history anymore.
- **D3 (legacy HTTP + CLI):** Remove the experimental `chat-context`
POST/DELETE endpoints, the agentsdk methods, and the CLI one-shot. The
dRPC push + `chat-context/refresh` replace them.
- **D4 (frontend fallback):** Remove the `last_injected_context`
fallback in `ContextUsageIndicator`; pinned `resources` are the sole
source.
- **D5 (sequencing):** Ship as a single PR rather than a stacked pair.

</details>

---
Coder Agents generated on behalf of @kylecarbs.

coderd/database/db2sdk/db2sdk.go

@@ -1752,17 +1752,6 @@ func Chat(c database.Chat, diffStatus *database.ChatDiffStatus, files []database
 			})
 		}
 	}
-	if c.LastInjectedContext.Valid {
-		var parts []codersdk.ChatMessagePart
-		// Internal fields are stripped at write time in
-		// chatd.updateLastInjectedContext, so no
-		// StripInternal call is needed here. Unmarshal
-		// errors are suppressed — the column is written by
-		// us with a known schema.
-		if err := json.Unmarshal(c.LastInjectedContext.RawMessage, &parts); err == nil {
-			chat.LastInjectedContext = parts
-		}
-	}
 	// Report pinned-context state when the chat is context-tracked
 	// (has a pinned hash), dirty, or carries a snapshot error.
 	if len(c.ContextAggregateHash) > 0 || c.ContextDirtySince.Valid || c.ContextError != "" {

coderd/database/db2sdk/db2sdk_test.go

@@ -720,13 +720,6 @@ func TestChat_AllFieldsPopulated(t *testing.T) {
 		PlanMode:          database.NullChatPlanMode{ChatPlanMode: database.ChatPlanModePlan, Valid: true},
 		MCPServerIDs:      []uuid.UUID{uuid.New()},
 		Labels:            database.StringMap{"env": "prod"},
-		LastInjectedContext: pqtype.NullRawMessage{
-			// Use a context-file part to verify internal
-			// fields are not present (they are stripped at
-			// write time by chatd, not at read time).
-			RawMessage: json.RawMessage(`[{"type":"context-file","context_file_path":"/AGENTS.md"}]`),
-			Valid:      true,
-		},
 		DynamicTools: pqtype.NullRawMessage{
 			RawMessage: json.RawMessage(`[{"name":"tool1","description":"test tool","inputSchema":{"type":"object"}}]`),
 			Valid:      true,