Why cookies do not allow authorization?

Question

HTTP Cookies

Situation: for some time now, a site on a subdomain does not authorize users until you delete some cookies (or all, or until you enter a private browser window).
Cookies that interfere with authorization are circled in red in the picture. They appear if you come to the site from the main site (without subdomains). If you delete all cookies, or those circled in red, then everything works. What to do, where to dig?