what is actually meant by that? when a url is requested ...

Basically its this use YouApp; YourApp->to_psgi; where to_psgi returns an $app

This shouldn't result in DBI->connect being called; If it does docs say don't use preload

Then later when a user makes http request to .../foo $app->() gets called

But to be sure if it can work or not, try it

also calling connect_cached would cause any problems under a preforked server like starman?

Probably not, but its easy to test

Remember to turn on https://metacpan.org/pod/DBI#AutoInactiveDestroy