From the first link:
White flashing volume lights
Unplug HomePod from its power source, wait 15 seconds, then plug it back in. If the white volume lights continue flashing, reset your HomePod. If these steps haven't resolved your issue, contact Apple Support to arrange a repair.
Without having a more detailed description (or your unlinked video) it was still possible the information might have been useful to you. FWIW I have a dead OG HomePod too. The volume lights flash once 13 seconds after power up and the unit restarts. If I press the top to reset it during start up the light turns red, but the volume lights still flash at 13 seconds and it starts over. It is outside its warranty so Apple aren't interested unless I want to pay the full cost for a repair. I did consider trying to exercise consumer rights options through the seller, Argos, but that involves investing in an independent assessment from a third party, which might be time and money down the drain. Argos could still say no, and they are bigger than me. At this stage I'm kind of resigned to it, but it still smarts. Sorry to hear that you've been unlucky too. 😕
tt2