How to stop google analytics from setting _ga cross-site cookie when using resources from site A on Site B

Question

I have a website (A) example.com on which I've placed google analytics tag.

I have a second website (B) property.com on which I am loading resources from subdomain.example.com.

When I visit site A (exaple.com), google analytics drop a cookie "_ga" with id "123" and domain "example.com".

Then I go to site B (property.com), and google analytics drops a new cookie _ga with id "456", HOWEVER the same "_ga" cookie with id "123" and domain ".example.com" is kept.

This happens because some resources from "subdomain.example.com" domain are loaded on "property.com".

The question is - how do I prevent this???

I've tried so far everything possible, without luck. I'll list my attempts and failures.

1. Modified the google analytics script to have a specific domain

   // For example.com

   gtag('config', 'GA_TRACKING_ID', {
   
       'cookie_domain': 'example.com'
   });
   

Result - nothing

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2. Nginx configuration file set to:

proxy_cookie_path / "/; SameSite=Strict; Secure";

Result - nothing

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3. Nginx configuration file set to:

add_header Set-Cookie "_ga=; Domain=.example.com; Path=/; SameSite=Strict";

Result the same cookie from .exmaple.com appears on proprty.com

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4.Nginx configuration file set to:

add_header Set-Cookie "_ga=deleted; Domain=.example.com; Path=/; Expires=Thu, 01 Jan 1970 00:00:00 GMT";

Result: the same cookie from .exmaple.com appears on proprty.com only this time the value is "deleted"

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5. Nginx configuration file set to:

proxy_set_header Set-Cookie "_ga=deleted; Path=/; Expires=Thu, 01 Jan 1970 00:00:00 GMT";

Result: similar to above point 4

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6.Nginx configuration file set to:

proxy_cookie_flags _ga SameSite=Strict Secure;

Result: apperently my nginx version doesn't support that, but something tells me this won't work as well.

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Obviously I'm trying to control this behavior from the (A) example.com domain, and offer my resources without spamming other websites with google/facebook cookies.

Please help, ChatGPT couldn't and I couldn't find an answer here.