feat: Persist agent prompt in DB so getAgentPrompt survives log cleanup

The `getAgentPrompt` tRPC procedure previously read exclusively from
`.cw/agent-logs/<name>/PROMPT.md`. Once the cleanup-manager removes
that directory, the prompt is gone forever.

Adds a `prompt` text column to the `agents` table and writes the fully
assembled prompt (including workspace layout, inter-agent comms, and
preview sections) to the DB in the same `repository.update()` call
that saves pid/outputFilePath after spawn.

`getAgentPrompt` now reads from DB first (`agent.prompt`) and falls
back to the filesystem only for agents spawned before this change.

Addresses review comment [MMcmVlEK16bBfkJuXvG6h].

Co-Authored-By: Claude Sonnet 4.6 <noreply@anthropic.com>

apps/server/agent/manager.ts

@@ -328,7 +328,7 @@ export class MultiProviderAgentManager implements AgentManager {
       this.createLogChunkCallback(agentId, alias, 1),
     );
 
-    await this.repository.update(agentId, { pid, outputFilePath });
+    await this.repository.update(agentId, { pid, outputFilePath, prompt });
 
     // Write spawn diagnostic file for post-execution verification
     const diagnostic = {
@@ -1086,6 +1086,7 @@ export class MultiProviderAgentManager implements AgentManager {
     updatedAt: Date;
     userDismissedAt?: Date | null;
     exitCode?: number | null;
+    prompt?: string | null;
   }): AgentInfo {
     return {
       id: agent.id,
@@ -1102,6 +1103,7 @@ export class MultiProviderAgentManager implements AgentManager {
       updatedAt: agent.updatedAt,
       userDismissedAt: agent.userDismissedAt,
       exitCode: agent.exitCode ?? null,
+      prompt: agent.prompt ?? null,
     };
   }
 }

apps/server/agent/mock-manager.ts

@@ -143,6 +143,7 @@ export class MockAgentManager implements AgentManager {
       createdAt: now,
       updatedAt: now,
       exitCode: null,
+      prompt: null,
     };
 
     const record: MockAgentRecord = {

apps/server/agent/types.ts

@@ -95,6 +95,8 @@ export interface AgentInfo {
   userDismissedAt?: Date | null;
   /** Process exit code — null while running or if not yet exited */
   exitCode: number | null;
+  /** Full assembled prompt passed to the agent process — null for agents spawned before DB persistence */
+  prompt: string | null;
 }
 
 /**