feat: add last_injected_context column to chats table (#23798)

Adds a nullable JSONB column `last_injected_context` to the `chats`
table that stores the most recently persisted injected context parts
(AGENTS.md context-file and skill message parts). The column is updated
only when `persistInstructionFiles()` runs — on first workspace attach
or when the agent changes — so there are no redundant writes on
subsequent turns.

Internal fields (`ContextFileContent`, `ContextFileOS`,
`ContextFileDirectory`, `SkillDir`) are stripped at write time so the
column only holds small metadata. No stripping needed on the read path.

<details>
<summary>Implementation notes</summary>

- New migration `000456` adds nullable `last_injected_context JSONB`
column.
- New SQL query `UpdateChatLastInjectedContext` writes the column
without touching `updated_at`.
- `persistInstructionFiles()` strips internal fields from parts via
`StripInternal()` before persisting.
- Sentinel path (no AGENTS.md) persists skill-only parts when skills
exist.
- `codersdk.Chat` exposes `LastInjectedContext []ChatMessagePart`
(omitempty).
- `db2sdk.Chat()` passes through the already-clean data.

</details>

site/src/api/typesGenerated.ts

@@ -1200,6 +1200,13 @@ export interface Chat {
 	 * connect and disconnect.
 	 */
 	readonly has_unread: boolean;
+	/**
+	 * LastInjectedContext holds the most recently persisted
+	 * injected context parts (AGENTS.md files and skills). It
+	 * is updated only when context changes — first workspace
+	 * attach or agent change.
+	 */
+	readonly last_injected_context?: readonly ChatMessagePart[];
 }
 
 // From codersdk/chats.go