Cloud storage when switching form Lightroom Classic to Lightroom

You know now how to wipe what's in the cloud now. You should not use the standard migration tool if you only want a subsection of your images from Classic to end up in cloud-based Lightroom. The migration tool will upload the entire classic catalog. There are many ways to accomplish that however. One way is to export a new catalog from your old catalog with just those images and collections you want in the cloud and to migrate that catalog. Another way is to export those images as originals from Classic and just drag those into cloud-based Lightroom. Yet another is to use classic to make your cloud selection (which gives you just smart previews in the cloud) and then drag the raws for those images into cloud-based Lightroom which will associate the raws with the already existing smart previews. 

There are a number of other methods but these are the most workable.

With Classic, only SmartPreviews for the synchronized collections are uploaded and stored in the cloud.

If you deactivate synchronization for all collections, that should clear them from the cloud ... give LrC some time to sync.

To verify and to also clear the trash bin in the cloud, log in to https://lightroom.adobe.com and clear everything out that may still be there. Once all is cleared, deactivate syncing in LrC.

That should give you a clear start to move the images to Lr.

Please make to set up Lr correctly before starting to move photos, as by default every photo you import is stored to the cloud. If you want to work locally, make sure to verify the settings first.

Use the integrated migration option in Lr to move from LrC to Lr.