It seems like you’ve done a lot of troubleshooting on your end to narrow it down to that. The way you’re describing the issue, I wonder if the problem is with the Doorbell (i.e., something on Wyze’s side) sending the button press signal or with Alexa (i.e., something on Amazon’s side) receiving the button press signal to initiate your routine on any other Alexa actions.
What happens when you go to the Doorbell’s Settings screen and tap the Restart Camera and/or Reset Services buttons? Does that have any effect? If the root of the issue is that the Doorbell isn’t sending the right server messages the way it should, then I wonder if that’s related to the notifications issue described in another topic and if periodic restarts (as noted beginning in the post linked below) provide some remediation:
Have you opened a ticket with Wyze Support? I generally find their advice to be unhelpful (especially compared to the user-to-user support available here), but at least opening a ticket is a way to get an issue tracked in Wyze’s system, and having a ticket number can sometimes help a community volunteer escalate an issue when the resources of the Forum have been exhausted.
Since I don’t have any experience integrating Wyze with Alexa (and I also don’t use iOS or Echo Show, though I don’t think your phone is part of the problem), I wonder if any @Mavens could provide some useful input or tag in another Forum user with the right kind of experience.