TYPO3 Core

TYPO3\CMS\Frontend\Controller\TypoScriptFrontendController

in function sendCacheHeaders()

$doCache = $this->isStaticCacheble();

and in function isStaticCacheble()
comments
"There can be no logged in user because user sessions are based on a cookie and thereby does not offer client caching a chance to know if the user is logged in."

$doCache = !$this->no_cache && !$this->isINTincScript() && !$this->isUserOrGroupSet();

But "$this->isUserOrGroupSet()" doesn't check if the user is logged in.
Therefore the exist of any frontenduser-session set "isStaticCacheble()" to false and "sendCacheHeaders()" sends "Cache-Control: private, no-store".

imho the change from

$doCache = !$this->no_cache && !$this->isINTincScript() && !$this->isUserOrGroupSet();

$doCache = !$this->no_cache && !$this->isINTincScript() && !$this->loginUser;

can solve this problem.