Why is the cookie not shown in devtools, while it is sent to the server?

Question

User identification

The client spins on the domain example.com
2 backends
api.domain.com
auth.domain.com
From the client, an AJAX request is made to each of the backends, which in response set the Domain cookie, .domain.comi.e. for subdomains (so that they can see each other's cookies). On subsequent requests for backends, cookies are successfully displayed in the debug console, i.e. the server sees them. At the same time, they are not displayed in DevTools, if you open them on the site example.comfrom where the request comes from.
What is it?
APD: funny. If, in addition to the AJAX request, I use a file from the domain, domain.comthen cookies appear! I am confused.
Full shiz. I found a bunch of issues with the same question - https://stackoverflow.com/questions/53495230/cooki...
Is this a feature?