Not too sure if there are any stores outside that would fix HomePods.
Both of my HomePods had the same issue. Out of the blue, it just gone dead. Turning off and back on the wall plug/switch doesn’t work.
Had also tried sending at the Apple Store in SG, but unfortunately they don’t service/repair or take in - and was told to send it in at Apple Store where the country sells them.
Did so in the US, and so far it’s mix between they can fix it at a cost, that might as well get the HomePod 2nd Gen or just trade it in - for the 2nd Gen.