Treat the move as a split, not a switch. Announce in the server what lives where: Discord for daily chat, the site for content, courses and payments. Link between them often. When someone asks a question in chat that has been answered before, answer with a link to the topic on the site.
Build the forum around the threads people keep asking about. Turn the most-asked questions and guides into topics, and map your channel groups to Jetonomy spaces. A small, well-organised forum beats a large empty one.
There is not really a cut-over day. Watch which channels stay busy on Discord, because those genuinely belong there. Move paid roles to BuddyNext Pro membership plans when the site is ready, then retire the roles on Discord that the site now handles.