How do I send commands to Google Assistant using Siri on a HomePod?

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I want to use Siri on my HomePod to send commands to Google Assistant via Home Assistant; specifically, I want to replicate the configuration demonstrated in this video.

I have already set up the Google Assistant SDK integration and created an Assist pipeline that uses the Google Assistant SDK as the conversation agent.

My understanding of the documentation for using Assist on Apple devices is that I am to create a shortcut containing the Home Assistant iOS app's "Assist in app" option, then run that shortcut via Siri. On my iPhone, this opens the Home Assistant app to a modal where I can interact with Assist; on my HomePod, Siri prompts me to "continue on the companion device" before automatically opening the Home Assistant app on my iPhone to the aforementioned modal. In both cases, this is exactly the result I would expect given the name of the "Assist in app" action. It is not, however, the result demonstrated in the video, in which, using a HomePod, the user tells Siri "Hey Google", Siri prompts the user for further response, the user gives a command, and Siri responds to that command as if it were Google Assistant.

Here is an iCloud link to the shortcut I am using. A screenshot of the shortcut is attached to this post.

[slender fable]

Why?

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I have an Android TV. I use a Google Home Mini to switch between the TVs HDMI inputs without having to pick up the remote. Recently, the Google Home Mini has started to routinely disconnect from my Wi-Fi, essentially bricking it until I completely reset the device (as far as I know, it is not possible to simply change the device's Wi-Fi settings unless I can reach the device over Wi-Fi).

I would like to be able to use my HomePod to accomplish what I have previously been accomplishing with my Google Home Mini. I already use HomeKit for other smart home matters (in fact, my primary application of Home Assistant is to expose devices that do not natively support HomeKit to HomeKit); it would be nice to be able to do everything through the same voice assistant.

[weary lotus]

I’m sure I found this on the documentation somewhere, but this is the shortcut I use to control Assist: https://www.icloud.com/shortcuts/cb4199362f854fc7ad959a249d0e1586

That basically hooks up Home Assistant Assist to Siri, so if Home Assistant can control Google Home for you, then you’re set.

The other option is to use HomeKit Bridge to make your Google devices show up in HomeKit and then let Siri do it natively.