How to setup Access_Control_Allow_origin & From origin blocked by CORS in Nginx for Mageno 2 multi-Website store?

You need to set up CSP in your website. Check this Magento CSP doc

Create csp_whitelist.xml in your module loading the second website inside etc folder

<?xml version="1.0"?>
<csp_whitelist xmlns:xsi="http://www.w3.org/2001/XMLSchema-instance" xsi:noNamespaceSchemaLocation="urn:magento:module:Magento_Csp:etc/csp_whitelist.xsd">
    <policies>
        <policy id="font-src">
            <values>
                <value id="your-test-website" type="host">test.website.in</value>
            </values>
        </policy>
    </policies>
</csp_whitelist>

set the cross-origin in app/etc/env.php by changing the following parameter.

'x-frame-options' => 'CROSS-ORIGIN',

after changing flush your magento cache

php bin/magento c:f

Go to Content->Design->configurations

Click on edit link against your website.

apply a different them for each website.

now run these commands.

php bin/magento setup:upgrade

php bin/magento setup:di:compile

php bin/magento setup:static-content:deploy -f

php bin/magento c:f