Siri on Homepod vs. iPhone: How to resolve conflict / Make Siri activate on correct device?

Siri on Homepod vs. Siri on iPhone:

How to resolve this conflict? How to make Siri activate on the correct device?

My problem is that I am used to giving voice commands to my iPhone (Siri) such as "Resume Overcast app" (for playing my podcasts in Overcast) or "Search the web for XYZ".

Now, HomePod activates instead and "steals" the voice command to then issue a useless reply a la "Cannot open apps on Homepod" :/

This seems not to be much of an improvement, in fact, Siri has become much less usable since adding the HomePod to the setup.

How can I define which device to execute the command on? I have tried adding "...on iPhone" but Siri ignores it. Would be easy to give another name to the Homepod, not "Siri", such as replaching "hey Siri" with "hey HomePod" but there seems to be no option for that?

What solutions options do I have? Other then returning the HomePod, disconnecting them, or pressing a physical button (which sort of defeats the hands-free purpose of voice commands), I am aware of those "options".

Essentially, I just want Siri to execute my command on the correct device.

Thank you for your thoughts!