Why doesn't CORS work in php?

Question

PHP

Please help me figure it out, I'm at an impasse.
Created a file /var/www/test/index.php.
Added it to nginx so that it can be accessed by test.local .
Created an index.html file that accesses test.local via AJAX.
I get an error that you can not contact a third-party domain.
Okay, really not, because there are no headers.
I put headers in index.php:

header('Access-Control-Allow-Origin: *');
header('Access-Control-Allow-Methods: GET, POST, PATCH, PUT, DELETE, OPTIONS');
header('Access-Control-Allow-Headers: Content-Type, Authorization, Access-Control-Allow-Methods, Access-Control-Request-Headers');

echo 'test';

The same. And if everywhere the asterisks put down the same thing and how I just did not try. And the headers are visible in chrome dev tools.
If these headers are written in the nginx config, then it works.
What's wrong?