I was able to add the Caséta Wireless fan control into both Lutron and HE, and I can control them there just fine. However, Alexa cannot discover the device. I have Caséta Wireless dimmers showing up in Alexa, so I've been able to migrate other devices over from HE into Alexa, just not the fan control.
This always refreshes my Alexa devices without fail.
I seem to recall, even simply renaming a device label, Alexa will update without refreshing that list.
I also created scenes in hubuitat to control the MyQ garage door because MyQ doesn't otherwise allow Alexa to open or close the door unless you're using Key. Just have to phrase it anything other than "Alexa, open garage door." I then created an Alexa Routine to open or close the door and give spoken feedback. Works great.