test(schema): add test for setting tool schemas with no argument input

internal/mcpserver/schema_test.go

@@ -13,6 +13,24 @@ import (
 	"git.warky.dev/wdevs/amcs/internal/tools"
 )
 
+func TestSetToolSchemasAddsEmptyPropertiesForNoArgInput(t *testing.T) {
+	type noArgInput struct{}
+	type anyOutput struct{}
+
+	tool := &mcp.Tool{Name: "no_args"}
+	if err := setToolSchemas[noArgInput, anyOutput](tool); err != nil {
+		t.Fatalf("set tool schemas: %v", err)
+	}
+
+	schema, ok := tool.InputSchema.(*jsonschema.Schema)
+	if !ok {
+		t.Fatalf("input schema type = %T, want *jsonschema.Schema", tool.InputSchema)
+	}
+	if schema.Properties == nil {
+		t.Fatal("input schema missing properties: strict MCP clients require properties:{} on object schemas")
+	}
+}
+
 func TestSetToolSchemasUsesStringUUIDsInListOutput(t *testing.T) {
 	tool := &mcp.Tool{Name: "list_thoughts"}