Can I use a HomePod on a Personal Hotspot (no WiFi available, only cellular)

Thanks for the info, If I understand correctly, the HomePod will itself play the Apple Music but I can’t stream, say, a third party app like TuneIn Pro to stream from the iPhone (Hotspot) to the HomePod.

That was my experience. I don't use Apple Music, but the HomePod can also stream music from your past iTunes purchases and it did this without any trouble (but I prefer to AirPlay from my own playlists on my iPhone). When I tried AirPlay from my iPhone, which was also serving as the hotspot, audio would stop playing after a few minutes regardless of the audio source on my iPhone (Amazon Music, Netflix, YouTube, or the on-board Music library synced from iTunes).

I’m assuming, as you seem to have implied, that if I have the iPhone as the Hotspot provider (typically sitting at a window with the best cell signal), I could still stream from my iPad Pro (also on the Hotspot) to the AirPod. Since both iPhone and iPad are the same Apple ID there should be no connection problem I guess.

Yes. In my case I would use my wife's iPhone as the hotspot, then put my iPhone into Airplane mode (but turn Wi-Fi back on and connect to her hotspot ... no jokes please ;-). Under these conditions, my iPhone could AirPlay anything without interruption. I didn't try my iPad in place of my iPhone, but I see no reason why that would not work since my iPhone had cellular turned off.

Recapping as I understand it: iPhone creates the Hotspot, iPad Pro is the audio source (iTunes Music or otherwise(?)) and the HomePod is the AirPlay speaker connected to the iPad Pro.

Yes, exactly.

When I moved into a new (well, old) house in the country last year I did this until I finally got internet service set up. While a hotspot works, what you'll find is that you cannot AirPlay from the iPhone to the HomePod -- it will work for a few minutes, then stop playing. IIRC, Apple Music directly from the HomePod works, just AirPlay from an iPhone doesn't if its being used as the hotspot.

If you want to AirPlay to the HomePod using a hotspot you'll need two iOS devices -- one as the provider of the hotspot, and the other connected to the hotspot as the source of audio for the HomePod. That worked fine, but I think that the Apple ID used for setting up the HomePod should be the ID that's on the device used as the audio source (can't remember why that was, maybe it isn't an issue if you open up the HomePod to accept connections from anyone).