Downloading Siri voice while watch is charging

Well that should happen instantly and actually on the iPhone. Go to Settings > Siri & Search > select English (or one of the main languages anyway and then tap on the different voices. If you are connected to Wi-Fi you should hear the sample and see the downloads starting right away there.

My apologies, I didn't realise the watch has these more extensive Siri settings hiding here under Settings - which are not shown in the Watch app at all. I could now see and recreate the same problem on my S6 too.

Even with the watch fully charged and sitting on the charger, that download does not seem to go anywhere to start with - the wheel just spins. However, I managed to make it budge and push forward, by switching the Wi-Fi network. Another benefiting factor might have been putting the fully charged watch back to my arm briefly as well.

I can imagine this part will be even more sluggish on earlier models and a slower network. Presumably each voice is over 100Mb in size after all. It would then be useful to know how to delete a downloaded voice too.

So try those things and hopefully it starts working for you too. There is either some initial setup time or some funky trigger sequence that allows the downloads to start. The next one will be swifter already.