So far I am getting the same instructions as before with SurfSpot: contact Adobe through chat etc.
I have another question: if I don't manage to delete the previous plan at all, will it disappear by itself after some period of time has passed? Or will the fact I'm not paying for that plan result in termination of my account including the current plan?
Streeploos, I am very sorry that you have encountered a confusing experience within this public discussion thread. As suggested by Shivangi, you can use the process listed in https://helpx.adobe.com/manage-account/using/cancel-subscription.html to cancel your individual membership through Adobe. Please make sure you are logging in with the same e-mail address you used to post to this public discussion forum.
The new membership that you are being provided by SurfSpot is a Creative Cloud Enterprise membership. As has been suggested we would encourage you to contact SurfSpot for information on how you can move over any files or assets to the membership that is being managed by them.
Alternately, you can also use the process listed in https://helpx.adobe.com/enterprise/kb/transfer-assets.html to manually transfer any files or assets from your current individual account to the new Enterprise membership managed by SurfSpot.
I am will now move this public discussion back to the Enterprise & Teams forum. The community in that forum may have additional suggestions for best practices as you transition from an individual Creative Cloud membership to an Adobe for Enterprise membership.