Restoring Time Machine Backup of an external hard drive that has failed?

That was so fast! And helpful! I located the data in Time Machine, and was able to select the new hardware as the destination. It's 'preparing to copy' as we speak, so fingers cross it manages to move everything successfully! Thank you - I'll update this thread if it works!

So your advice worked in terms of finding and transferring the backups from the old external drive to the new one. I sincerely appreciate it. Two other interesting problems came up in the transfer that you may be able to assist with, or I can also start a new thread if needed.

1) Firstly, and less of an issue: the transfer was two large folders (with lots of sub folders) and my photo app library. The two large folders (~2tb combined) transferred fine, but when I went to 'get info' to see how large they were (to compare them to the original file size) they were listed as zero KB. I left it open and waited for it to potentially update, but nothing. I dug deep into the subfolders and checked some folder sizes there, and the deepest subfolders would update, which would then update their parent folders. I basically went through the entire file directory doing that until the upper most container folder read a file size that was roughly what the original backed up folder was. Any idea how to get this folder to accurately read it's overall size? I am assuming the index of the drive wasn't updating, but no amount of restarting or remounting the drive made a difference.

2) A bigger problem: the photo app library would not transfer. All the other folders in the backup transferred, but on the transfer of the photo library I received this error: "The Finder can’t complete the operation because some data in “Photos Library” can’t be read or written. (Error code -36)". I've tried several times, with several versions of the backup going back a month or two, but I get the same message each time. Any advice on getting this folder transferred so I can attempt to repair it? For reference the folder in ~250gb. Sincere apprecation and let me know if I should start a new thread, as this is a different problem.