Thanks for the clarification. my mistake on privacy being your concern. Disregard my mention of privacy. And I understand when something tech doesn't work as expected repeatedly, it can be frustrating.
First piece of assistance is check the Apple Support document. it may have something of value: Get help with Siri on your iPhone, iPad, or iPod touch - Apple Support
My second suggestion: On your iPhone press the Home app, long press the HomePod button, scroll down to the bottom and press the Settings button, scroll down to near the bottom and make sure 'Personal Requests' is enabled. (afterwards I'd consider then hitting the Restart HomePod that is just below).
If this didn't fix it, next with your iPhone, try moving far enough away from the HomePod and ask "hey Siri, what is the temperature outside". Does the Siri request work on your iPhone?
Last suggestion, I ran into something similar when I first got my HomePods. It worked good for me but with my GF, Siri would respond to some of her requests but wouldn't respond to others (but I believe she would get 'not available right now', not the message you receive). It was because she was not a recognized member of 'my home' network. It is a bit of a process to accomplish but is it possible it doesn't see you as the primary Home Network user? Here's a doc about having multiple people use Siri: https://appletoolbox.com/siri-multiple-people/