Welcome to the Forum, @haffey! 
Have you tried enabling the VoIP option for the doorbell? That’s one feature many users employ to differentiate doorbell button presses from other Wyze notifications. With the number of notifications you say you’re getting—which it seems as if you likely ignore because of the frequency and false positives—I’d also consider decreasing motion sensitivity in order to mitigate some of the notification overload you seem to be experiencing.
What you’re requesting has actually been a Wishlist request for some time:
You can pop over to that topic, click the Vote button above the initial post, and share your ideas and use cases in the comments.
If you identified as an Android app user, then I’d suggest ways to use third-party notification interceptors in order to customize your doorbell button press notifications. Unfortunately, I’m not aware of a way to do this on iOS, and I completely agree that Wyze should build this into the app as an option for both platforms (and I’ve voted for that particular Wishlist item); however, I recently learned that Apple may have to open up some notifications features (among other things) in order to comply with the European Union’s Digital Markets Act, and since the rules are supposed to benefit both device and app developers, then I would expect enterprising third-party iOS app creators to exploit the opening and create tools that give iOS users some notification flexibility similar to what Android users have been able to enjoy for some time. If or when that might actually happen is anyone’s guess, though. 
That’s the plan, though I’m not yet aware of a specific delivery date. The Wi-Fi Chime that was introduced with Duo Cam Doorbell was announced for potential separate availability as soon as December 2024:
My sense is that Wyze is still working out details (and I suspect inventory) for this, so I don’t know when it’s supposed to happen, but that device is compatible with other Wyze doorbell and camera models.
You also said this:
Which models of Wyze Cam do you have? If you have either of the Cam OGs (Standard or Telephoto), Cam Pan v3, or (I believe) Cam v3, then you should be able to enable any or all of those as accessory chimes for your Vieo Doorbell v2. I use some Cam OGs and a Cam Pan v3 for that purpose.