rest_authorization.php

<?php

function rest_authorization( WP_REST_Request $request ) {
    $log = trim( $request->get_param( 'log' ) );
    $psw = trim( $request->get_param( 'psw' ) );

    $errors = [
        'status' => false,
        'text'   => '',
        'fields' => [
            'log' => '',
            'psw' => '',
        ],
    ];

    if ( ! $log || ! $psw ) {
        $errors['text'] .= ! $log ? __( '<strong>ERROR</strong>: The username field is empty.' ) . '<br>' : '';
        $errors['text'] .= ! $psw ? __( '<strong>ERROR</strong>: The password field is empty.' ) : '';

        $errors['fields']['log'] = empty( $log );
        $errors['fields']['psw'] = empty( $psw );

        return $errors;
    }

    $user = wp_signon( [
        'user_login'    => $log,
        'user_password' => $psw,
        'remember'      => 1,
    ] );

    if ( is_wp_error( $user ) ) {
        $code = $user->get_error_code();

        return wp_parse_args( [
            'text'   => preg_replace( '/<a.+a>/', '', $user->get_error_message() ),
            'fields' => [
                'log' => 'invalid_username' == $code,
                'psw' => 'incorrect_password' == $code,
            ],
        ], $errors );
    }

    return [ 'status' => true ];
}