The built-in hue integration is primarily for controlling lights from within HE, with the expectation that you configure any scenes within HE and/or utilize sensors and controllers paired with HE, even in addition to automations configured on the hue bridge. It has been this way almost from the beginning.
The recommendation to pair bulbs and accessories to the bridge, I believe, is primarily for older models that I think pre-date the zigbee 3.0 varieties, as there were some differences in the way they would relay messages to other devices in the mesh if paired with HE. I still have mine paired to my bridge.
Some time ago now @bertabcd1234 developed Coco-Hue and @armand developed Advanced Hue Bridge Integration to, amongst other things, allow control of scenes defined on the bridge.
In recent times Philips have developed a new API that both @bertabcd1234 and @armand have made use of to receive events from the hue bridge when, amongst other things, a button controller is pressed or a motion sensor is activated. This allows what you are wanting to see, the press of a button for a device paired with the hue bridge to come through to HE for use in automations.
I'd suggest taking a look at these integrations.
