Sounds like your TM isn’t big enough. By dragging the folder out of the TM backup, you’ve forced TM to treat the copied folder as a brand new drive, on top of the backup that you’ve already got of the dead drive – doubling the amount of TM space needed for the same data. If you’re certain you’ve got all your files back, format your TM drive and start it as brand new backup. OR – get yourself a new TM drive that’s much bigger and store the old TM drive labeled neatly with today’s date. I recommend the latter as you’ll always be able to return to this date with your data.
Drives die, so extra backups of old data is never a bad thing.