@William Kucharaki: Thanks for explaining this issue in detail. For example, the suggestion, turning on the USB Accessories option in settings does not work out quite well for me; at least it is very unreliable (my iPhone XS sometimes refuses to charge after let's say 15 minutes of inactivity, too). But a double tap always forces the phone to start charging. A raise to way sometimes works, sometimes not. I only use the bundled cable and charger. To be said, I did not try to hard reset my device -- maybe that's also worth a try?
It seems like that the custom handshake between charger and device is not implemented correctly in power management, particularly in regard with the "new" security feature of iOS.
As for now, I can live with the issue, as I use wireless charging or quickly activate the display before charging via cable. So at least there is a workaround and a good hope that Apple is able to fix this via Software Update.