Okay, so, an update after last night’s fiddling
I tried:
Sky > (HDMI IN) soundbar (HDMI ARC) < TV < Chromecast
No joy. Sound from Sky was fine, no sound from Chromecast
I then tried:
Sky > TV HDMI
Chromecast > TV HDMI
TV > Soundbar via optical cable
Sound from Chromecast was noticeably out, sound from Sky was a tiny bit out. There’s a sound delay tinkering feature on the soundbar, but I don’t want to be messing with that every time I switch source. There’s no latency fiddling option on the telly.
By that stage wifey was getting a bit peeved, so I left it.
Tonight’s final attempt is:
Chromecast > (HDMI IN) soundbar (HDMI ARC) < TV < Sky
on the probably naive assumption that the Chromecast input signal somehow doesn’t support CEC/ARC, but the Sky one does.
If that doesn’t work, it’s back to Plan A, and occasionally having to get off my arse to switch sources.