Headers already sent error with get_template_part in REST API call

Question

I've looked at multiple other questions about this warning (Headers already sent...etc) and this thorough explanation, but I'm not finding a solution for the circumstances I'm dealing with:

1. I have a custom Wordpress REST API endpoint that returns the output of get_template_part. When I just call get_template_part normally on a page, there's no warning. It only appears when it runs in register_rest_route's callback.
2. I am also fetching data from an external API using this library. The error started when I started making these requests. I've tried making the request both inside and outside the template part, the latter either within register_rest_route's callback or as an init action.
3. The line that triggers the error is an img tag, where I'm echo-ing a URL as the src using data from the external API response. There are other echo calls all over this template, so I doubt that's the issue.
4. The line in question actually works fine and does its job. I just need to get rid of the accursed warning.

Code:

Inside functions.php:

<?php

  //the api endpoint declaration
  add_action( 'rest_api_init', function () {
    register_rest_route(
        'theme/v2',   // namespace
        '/homepage',  // route
        array(                  // options
            'methods'  => 'GET',
            'callback' => 'build_home',
        )
    );
  });

  //the callback for the wordpress api
  function build_home() {

    // this is the external API request, using their PHP library. 
    // I linked the library above. The request returns an object with a bunch of data
    include_once(get_template_directory()."/arena/arena.php");
    $arena = new Arena();
    $page = $arena->set_page(); 
    $per = 8; 
    $slug = 'concepts-bo-6ajlvpqg'; 
    $channel = $arena->get_channel($slug, array('page' => $page, 'per' => $per));

    //I'm passing the response from the external API (in $channel) to get_template part
    //get_template_part is then the output for the wordpress API request
    get_template_part('custom-home-template',null,array('channel'=>$channel));
 }

 ?>

Inside template part:

<?php
  $channel=$args["channel"];
  ?>

  <div id="concepts-box" class="bodycontent reg-width">
    <?php foreach ($channel->contents as $item) { if($item->class=="Image"){
      $img=$item->image["square"]["url"];
      ?>
    <div class="concept-wrapper">
      <!-- the line below is the one that triggers the error -->
      <img lozad src="<?=$img; ?>">
    </div>
    <?php }} ?>
  </div>

Full warning:

<b>Warning</b>:  Cannot modify header information - headers already sent by (output started at /filepath/wp-content/themes/theme/custom-home-template.php:63) in <b>/filepath/wp-includes/rest-api/class-wp-rest-server.php</b> on line <b>1372</b><br />

Answer 1

Answered on Wordpress SO — link here. The issue was I was treating get_template_part as an API response instead of feeding it through output buffering into a variable