The new attributes are called secure and SameSite. I am just now reading about them myself but here is what i know so far.
First here is an example of the warning you will get from google tools.
A cookie associated with a cross-site resource at http://google.com/ was set without the `SameSite` attribute. A future release of Chrome will only deliver cookies with cross-site requests if they are set with `SameSite=None` and `Secure`. You can review cookies in developer tools under Application>Storage>Cookies and see more details at https://www.chromestatus.com/feature/5088147346030592 and https://www.chromestatus.com/feature/5633521622188032.
Here is the techical reference:
https://www.php.net/manual/en/session.security.ini.php
Here is a snippet text from that page.
As of PHP 7.3 the "SameSite" attribute can be set for the session ID cookie. This attribute is a way to mitigate CSRF (Cross Site Request Forgery) attacks. The difference between Lax and Strict is the accessibility of the cookie in requests originating from another registrable domain
I do need to mention that this particular warning from google listed above is from google, there is nothing site owners can do about it, its up to google to change their code is what im thinking. But please correct me if i am wrong.
These warnings from google are caused by including some of the snippet code from google you may have in your site custom headers. You might want to check if google has new or updated snippets with the additional attributes included.