Not the full binding functionality, but you can just have the Axis make a HTTP GET request to an item in OpenHAB to trigger something when pressed. Not familiar with the doorbell specifically, but their camera’s have this ability on events. So you can define an event for motion detection and use the doorbell button as a trigger to make web calls to separate OpenHAB items via the legacy (unsupported and bad practice from RESTful standards) endpoint: http://localhost:8080/classicui/CMD?<itemname>=<command> .
So you’d make an item like Trigger_DoorbellPressed and make the doorbell do a call to http://openhab:8080/classicui/CMD?Trigger_DoorbellPressed=ON
Note that this CMD? endpoint could go unsupported and the REST API is the preferred method, but I don’t think you can do a HTTP GET to set an item in the REST API and I don’t think the Axis stuff with do a PUT
See this guide section 2.3 for setting up the HTTP event action
and this post for more information on the CMD? endpoint