If the new drive doesn't yet have any cataloged images on it, LR won't see it until it does. You can use the Folders Panel to add a top-level folder on the new drive, then of course it will show in the panel.
The standard advice is indeed "move images within Lightroom", but in the situation where you're planning to move everything off a bunch of drives to one big new drive, this is where I personally would NOT do it within Lightroom (because of the risk of something going wrong mid-move). Instead I would COPY the data, a drive at a time, to the new drive, outside Lightroom, but maintaining the current folder structure for each drive. After each drive, or at the end when all data has been copied, start Lightroom (everything will be unchanged), then right-click on the top-level folder on drive 1 and select "Update Folder Location". A file browser window opens, use this to navigate to and select the copy of that top-level folder on the new drive. That will update the LR database, the new drive will appear and the old drive should disappear (unless there are more top-level folders on the old drive, in which case repeat until done). Do that for all the other drives, and you should end up with the desired goal.
Any subsequent folder manipulation you want to do, e.g. to consolidate folder structures under one master parent folder, can then be done inside LR, as that won't involve moving any data so should be quick and relatively risk free.