Pretty straight forward question:
Is it possible (Today- Summer '20) to include an "Experience Builder Page", non-default, created from Experience Builder in a package (managed or unmanaged)?
You can export the page from the Experience Builder Developer Section as shown below and then you should see it in both Managed and Unmanaged package.
The exported page will be available in the changeset under Lightning Page component. It will be in below format
[Site_Name]_[Exported_Page_Name]
Ex: Get_Support_Account_Management