feat(web): conversation management — search, rename, delete, archive (#121)

- Add search/filter input to sidebar that filters conversations by title
- Add rename via double-click or context menu (right-click), confirmed with Enter or blur
- Add delete with inline confirmation dialog in context menu
- Add archive/unarchive via context menu with collapsible archived section
- Add auto-title: generates conversation title from first message content
- Show relative timestamps (e.g. "2h ago", "Yesterday") instead of raw dates
- Extend Conversation type with `archived` boolean field
- Add `archived` column + index to conversations DB schema (migration 0001)
- Extend UpdateConversationDto with optional `archived` field

Fixes #121

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

apps/gateway/src/conversations/conversations.dto.ts

@@ -1,4 +1,12 @@
-import { IsIn, IsObject, IsOptional, IsString, IsUUID, MaxLength } from 'class-validator';
+import {
+  IsBoolean,
+  IsIn,
+  IsObject,
+  IsOptional,
+  IsString,
+  IsUUID,
+  MaxLength,
+} from 'class-validator';
 
 export class CreateConversationDto {
   @IsOptional()
@@ -20,6 +28,10 @@ export class UpdateConversationDto {
   @IsOptional()
   @IsUUID()
   projectId?: string | null;
+
+  @IsOptional()
+  @IsBoolean()
+  archived?: boolean;
 }
 
 export class SendMessageDto {