Solution:
install the app not with Capabilities, but in the runtime with ((InteractsWithApps) driver).installApp().
WebDriverAgent can get all the necessary system-level interactions. Such as are Apple secure SpringBoard Passcode prompts.
Attention: For me it was necessary to install the runtimeApp with different bundleID, Appium somehow cached the Dump and if I have simply updated the capabilityinstalled app with runtime - it did not work.