The absence of a search button in the Messages app on the POCO C71 is due to the version of Google Messages pre-installed on the device, which is the "Go" version.
For your reference, here are more details of the issue:
1. The Google Messages Go version is a lightweight version of the app designed to use fewer resources and offer a simplified experience. As part of this design, certain features, such as the search function, are not included in the Go version;
2. This is a design choice by Google, and it is not a problem with the POCO C71 itself. The phone is fully functional, and you can still send, receive, and manage messages normally, but without the search capability in the Messages app.