I don’t know which camera models you have in boxes or installed, but the Video Doorbell v2 can also use some cameras as accessory chimes. As far as I know, that feature is currently available only for Cam OG and Cam Pan v3, but Wyze says there are plans to extend that feature to other cameras.
I’m not aware of any plans to develop this function for the original Video Doorbell (v1) as a setting within the doorbell itself, but I imagine it would be possible with a Rule of Device & Service Trigger type. I would’ve suggested that this might be possible with Rules, but I’m not currently seeing “Ring” as an available Action for either the OG or Cam Pan v3, and I don’t know when that was removed. (I also don’t know if “Is pressed” is available as a Trigger for the original Video Doorbell—as it is with the Video Doorbell v2—but I would expect that to be the case.)