I’m not the OP but I see the connection as Google seeking growth and revenue by applying their general search know-how to areas outside of the Internet.

I followed search appliance closely when they announced it. It was interesting technically and looked cool, but seemed like a dead end similar to desktop as applications were largely moving off of racks/desktops. I was right about that, but I expected Google to offer a web-based search appliance and they never did beyond custom searches. Algolia fills that opportunity nicely now.

There was an Enterprise version of the Desktop app that connected to the Google Search Appliance (yellow pizzabox) or Google Mini (blue pizzabox, not Google Home Mini) as well as searching Windows/Mac local/shared drives https://web.archive.org/web/20070302151851/https://desktop.g...

I'm guessing, I think the box was marketed as a networked version of the app, and GP might be drawing a bit hand-wavy connection between the two.