fix: build manifest image during create_instance instead of start_instance

The manifest-based flow was building the Docker image inside start_instance,
which made the start HTTP request take 3-5 minutes (downloading ubuntu:24.04,
apt-get update, installing packages, Node.js, npm packages). The frontend
showed a spinner forever because the HTTP request was still pending.

Move the image build to create_instance (same pattern as dockerfile types):
1. create_instance now compiles Dockerfile + entrypoint and builds the image
2. start_instance sees the image already exists and skips the build
3. Start is fast — just docker compose up + health checks

This matches the UX expectation: creation has a spinner (can be slow),
start should be quick.

apps/api/src/api/tool_instances.py

@@ -748,7 +748,7 @@ services:
             write_compose_file(instance_dir, compose_content)
 
         elif tool_type.definition_type == "manifest":
-            # Manifest-based: generate compose from manifest definition
+            # Manifest-based: build image and generate compose
             from src.models.tool_definition_manifest import ToolDefinitionManifest
 
             manifest_def = await session.get(
@@ -772,6 +772,39 @@ services:
 
             image_tag = compute_image_tag(tool_type.name, manifest)
 
+            # Build image during creation so start is fast
+            dockerfile = compile_dockerfile(manifest)
+            entrypoint = compile_entrypoint(manifest)
+            build_ctx = {
+                "Dockerfile": dockerfile,
+                ".headquarter/entrypoint.sh": entrypoint,
+            }
+
+            returncode, stdout, stderr = await asyncio.to_thread(
+                build_image,
+                instance_dir=instance_dir,
+                dockerfile=dockerfile,
+                tag=image_tag,
+                build_context=build_ctx,
+            )
+
+            if returncode != 0:
+                logger.error(
+                    "Failed to build image for manifest instance %s: %s",
+                    instance_name,
+                    stderr,
+                )
+                raise HTTPException(
+                    status_code=status.HTTP_500_INTERNAL_SERVER_ERROR,
+                    detail=f"Failed to build Docker image: {stderr[:500]}",
+                )
+
+            logger.info(
+                "Built manifest image %s for instance %s",
+                image_tag,
+                instance_name,
+            )
+
             variables = {
                 "IMAGE_TAG": image_tag,
                 "INSTANCE_NAME": instance_name.lower(),