Have you enabled the "Bridge Polling Option" under Options (in the Hue Bridge integration). The HE hub will not be able to save a scene, if it has not polled the Hue to get that scene. Any changes done by the HE Hub, the HE hub know about, but not anything done external to the HE Hub, for example from within the Hue app.
I dont use Alexa, but if it's the same as Google Home, you first need to select it from within the Alexa app. I presume this is what you mean when you say "the normal discovery method is not adding the scene". Then, in the Google home app, and I presume the Alexa app (not within HE hub, but the Alexa app itself) we then need to "refresh my devices" (this is google terminology). Then it adds all the new goodies.
Translate "refresh my devices" for Alexa, and you should be right.
I have not been able to make the hue scene work at all. Did u add single bulbs or hue groups. Also when you hit capture did all the settings (level hue and sat) populate like u showed above. When I hit capture none of the settings show.
I added the Hue Integration for both my Bridges. Then Created Scenes in HE and added devices (Select color and color temperature bulbs for scene) from Hue to those scenes. Capturing did not work for me until the next day for some reason. But now, I am able to go into the Hue App, chose a scene for the associated room devices, and it seems to capture fine on the HE. Then I added the scenes to be discovered by the Alexa Integration/HE Amazon Echo Skill as well as added HE Dashboard Buttons to activate each scene. I have noticed that it is better to give the HE time to poll the bulbs before trying to perform a recapture. I have my polling set to 10 seconds.
I actually now prefer this HE Integration method with Alexa to the Hue Skill. Because our home is large with hundreds of devices/bulbs/scenes, It gives me greater control over what shows up in Alexa where as before with the Hue Skill, everything showed up and it was just too much....
Alexa see scenes from the HE as devices though, that is a bit odd, but it works...