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>

coderd/database/dump.sql

@@ -1403,7 +1403,8 @@ CREATE TABLE chats (
     build_id uuid,
     agent_id uuid,
     pin_order integer DEFAULT 0 NOT NULL,
-    last_read_message_id bigint
+    last_read_message_id bigint,
+    last_injected_context jsonb
 );
 
 CREATE TABLE connection_logs (