Copying Time Machine Backup from one external drive to another - taking forever!!!

Answering on Kappy's behalf,

1. Can I do this same thing in High Sierra? Is it the same procedure with High Sierra?

Yes and yes.

2. Do I need to restart and enter Recovery mode,

No

... can I just do this using Disk Utility without having to be in Recovery mode?

Yes.

The capacity of the drive is not relevant; the amount of time to complete depends on the amount of data it actually needs to copy (the number of files and their size). "Preparing to copy" means it hasn't even started copying anything though. When it does it will take several more days to complete.

When transferring one Time Machine’s contents from one disk to another I find it much easier, faster, and more convenient to simply use Disk Utility’s Restore function: Restore a disk using Disk Utility on Mac - Apple Support. That’s what I do and that’s what I recommend.

The recommended way is to clone the existing Time Machine backup drive to the new backup drive which should be of larger capacity.

Clone El Capitan and Sierra using Disk Utility

1. Restart the computer and after the chime press and hold down the Command and R keys until the Utility Menu appears.
2. Select Disk Utility from the Utility Menu then press the Continue button.
3. Select the destination volume from the left side list.
4. Select Restore from the Edit menu of Disk Utility. A panel will drop down.
5. Select the source volume from the drop down menu in the panel.
6. Double-check you got it right, then click on the Restore button.

Destination means new Time Machine drive. Source means the old Time Machine drive.

Time Machine drives should only be formatted as GUID with a format of Mac OS Extended, Journaled. DO NOT use APFS.