What did you exactly say to HomePod Siri to silence the alarm on your iPhone? So far I've only been able to set and silence an alarm on the Homepod itself.
I must say, I understand why people don't like Siri that much. While it does recognises the spoken text very good, sometimes perfect. But really understanding is problematic. A few versions ago you could say "turn the light off" and the lights in the room where the Homepod was located are turned off. If you said "turn the lightS off" (plural) then the whole house was turned off. Now with Homepod version 15.4 you always need to say "turn the lights off" and the name of the room. Homepod Siri doesn't understand "in this room" even though the location is known.
Sometimes asking for a Homekit scene can suddenly result in a web search on my iPhone or an attempt to find a none-existent app on one of the AppleTV's. That can be very annoying.
I have problems with the "personal requests". The HomePod mini has no problem recognising each person in the house, but when my children ask for a playlist from their own account Siri is unable to find it. It always looks om my account. Even the person that is set as the primary user on specific HomePods still access my Apple Music library. But when that person asks Siri who's speaking then Siri answers correctly.
That sounds much like a local network problem. Its not uncommon that some wifi routers block some of the traffic between devices on the local network. Some don't even route properly between devices on 2,4GHz and others on 5GHz. Even small network switches can do bad things. Years ago I got this switch that didn't pass all traffic between 10M and 100M ethernet connectors. A serious circuit design fault that caused a lot of headages. And more recently I dumped a couple of Netgear switches (GS108 versions 1 en 2) that blocked some essential IPv6 traffic. Some mDNS / Bonjour traffic, but also random IPv6 internet traffic got blocked. When I contacted Netgear Support, they simply replied that the GS108 did not support IPv6. What the xxxx? That thing was supposed to be "dumb" and transparent for all kinds of network traffic. So I trashed them immediately and got a proper (and bigger) switch from Zyxel.
In my experience with a lot of Apple's Cloud services, when you have a slow internet connection it does help when you turn on iCloud caching on a Mac that is on the same network and is on for most of the day. It really does speed up many cloud things for all Homepods and other idevices on the network.