Thanks for the explanation, even if it’s not the answer I hoped to hear.
I have managed to get the iPad Air 2 playing audio into the HomePod, but didn’t do it via the Home app, so at least that’s one useful feature still working.
I didn’t knowingly upgrade to the new Home architecture. My original HomeKit setup was hosted on the old iPad Air, using a different iCloud account to mine, so that people using the iPad in the kitchen were unable to access my emails etc. Once I got the HomePod mini, I set it up in the normal way using my iPhone and then migrated each HomeKit device one by one, resetting it and then adding it to the Home app on my iPhone. I was also able to use some Matter enabled devices which the earlier version of Home would not recognise.
I had previously done searches for ways to migrate the existing HomeKit setup from one iCloud account to a different one, but couldn’t find anything, which is why I ended up doing it that way, starting afresh with one device at a time. Then I replicated the automations.
It seems a shame that older devices can no longer continue to do relatively simple tasks like acting as a display and remote control for a home automation setup, when my even older iPad was hosting the entire Home system.
Apple talks about how it recycles materials from old devices, but a much better form of recycling would be to re-use that old device in a useful role, but the current software doesn’t allow that.
Is there any third party app which could let the IOS15 device interact usefully with the new Home architecture? I’d be happy if it would just control a few lights and power.switches, nothing clever. Automations and Shortcuts can be handled on my iPhone and the HomePod in the usual way.