Import from collection to catalouge

Go to Preferences (Settings) - Lightroom Sync. There you can specify where synced images should be stored, so you can select a folder on your NAS. You can also specify if Lightroom Classic should create a dated folder hierarchy, just like you can in your import dialog. This will deal with new images. The images that are already downloaded can be moved to the NAS by dragging and dropping, just like what you can do with any other image. Edits and other metadata are stored in the catalog, so nothing happens to them. If there is an XMP file as well, then that file will be moved by the drag and drop action too.

If I understand correctly, the synced images from your iPad are now already in LrC. In which case they are now like any other images in LrC in that they can be moved from current location to any other location that appears in the Folders Panel. So select all the images that you want to move, then drag them to the folder of your choice in the Folders Panel.

Tip: to avoid having to keep doing that, you can change the download location for synced images via the LrC Preferences>Lightroom Sync tab, i.e. you can have them automatically stored in a folder on your NAS (and can even have them organised into dated sub-folders.