When I use “Hey Siri Assist” I get a response “How Can I Assist”. So far so good I guess. When I give her any command to turn on a light I get a response “ How Can I Assist”. This keeps happening in a loop over and over usually. One time I did get a response that the action wasn’t found. It was my understanding that Assist would work with any current automations out of the box. Do I need to edit my current automations to work with Assist?
After posting I realized that an update for Home Assistant was available. After installing Assist still isn’t working. The first time I tried “Hey Siri Assist” the response was “What’s Up”. 
After that I got the response shown in the attached screenshot.
For me iOS 16.3 with Home Assistant Companion App 2023.2 and Home Assistant 2023.2.2 my phone starts Home Assistant app when I say “Hey Siri, Assist” instead of asking “How can I assist” that should come from Shortcut.
There seem to be multiple issues. I installed HA 2023.2.2 and tested again.
“Hey Siri Assist” is just and endless loop. Every command I give is followed by “How can I assist”. Activating Assist using the triple dots in the iOS app works about 10% of the time if I type in the request. Usually I just get an “Sorry, I couldn’t understand that”. If I try to use the audio input by selecting the microphone symbol in the input field I get “Home Assistant did not hear anything” as an immediate response every time.
I guess HA really isn’t as serious as they claim about voice. They really make a big deal about it in their youtube videos. Disappointing that they don’t even respond to posts regarding issues.