I've recently upgraded to a Pixel 5, and I can't get notification replies from my Fenix 6 Pro to work reliably.
They seem to work if I have the phone unlocked, and Connect (or Hangouts - I'm testing with that) open, but if the phone is locked then although my Fenix 6 displays the "Reply Sent" confirmation, no reply is actually sent.
I've tried disabling all the battery optimisation stuff, still no joy though. It all worked as expected with my previous phone.