Why do Chromium and Chrome delete all cookies after closing the browser?

Session Cookies vs. Persistent Cookies

When creating a cookie, the code has the option of setting an expiration date & time. If this is done, then that cookie is persisted to storage on the client's web browser (e.g. it writes it to a cookie file ... the specific name for that file will vary based on which web browser is being used.)

If a cookie is created without setting an expiration time, then that cookie is a "session" cookie. It will not be stored in any file. It will only be stored in the web browser's process memory and will be dropped when that process ends.

See https://en.wikipedia.org/wiki/HTTP_cookie

Note there's some loose language in that Wikipedia article. A single browser process (any browser... Chrome, Chromium, Safari, Firefox, etc.) can have multiple windows and multiple tabs per window. Session cookies are only dropped when the browser process terminates ... not when the tab is closed. Most browser don't lock cookies to a specific window or tab (though there have been exceptions.) This means usually you can close a window or tab ... then re-open a new window or tab (as long as you didn't completely exit the browser) and return to a page without having to create a new session cookie.

Caveats

Cookies dealing with user sessions usually wont have an expiration time (making them "session" cookies) but the server session itself may have other attributes which track the maximum length of the session.

It is somewhat common for hosted applications to save the session creation time as well as the session idle time ... and set maximum elapsed times for those. This varies depending on the application -- it is not based on any standard. But the net effect is that just because your browser still has a cookie, doesn't mean a server will honor the cookie.