Unfortunately, Apple has made this pretty much impossible with their newest versions of macOS. The simple process of copying (or cloning) the drive to another one is not recommended as it typically results in a "broken" Time Machine backup set.
However, it can be attempted if those backups are critical to you ...
... and the following are the basic steps to do so. Again, I can't guarantee the results, so proceed at your own risk.
Step 1: Verify that your new drive has ample storage space for the current backup set. Overall, the drive's size should be 2-3x the total internal drive space of your Mac. Note: If you haven't purchased the new drive yet, I suggest that you consider getting a HDD over an SSD for this purpose for three reasons: 1) There is no real performance gain using a SSD for backups, 2) The effect of writing numerous files to a SSD will "wear" out its memory cells quickly rendering them unusable, and 3) HDDs are still far cheaper per GB than SSDs.
Step 2: Make an Exact (Clone) Copy of the Source Backup Drive.
- Do not use the Finder app to just copy the TM backup to the new drive. Instead you will two options to "clone" the backup to the new drive: 1) The Disk Utility, or 2) Via the Terminal app. Using the Disk Utility if far simpler, so let's go with that route.
- Open Disk Utility. It is located at: /Applications/Utilities.
- Select the New Drive in the left sidebar.
- Click the Erase button first, choose the correct format (APFS), and make sure the Scheme is set to: GUID Partition Map.
- Name the new drive something appropriate like NewTM.
- With the new drive selected, click Restore in the toolbar.
- For "Restore from:", choose your old Time Machine drive. Disk Utility will copy everything from the old to the new disk, byte for byte.
- Once done, unplug the old drive, plug in the new one.
Step 3: Add the new drive to Time Machine
- Go to System Settings > Time Machine
- Add the new drive if needed. macOS may automatically recognize the backup; if not, we will need to use the tmutil inheritbackup command in the Terminal.
That command would be: sudo tmutil inheritbackup /Volumes/NewTM/Backups.backupdb/YourMacName
Step 4: Test It!
Run a new Time Machine backup with the newly cloned drive and try restoring a file using the Time Machine interface to make sure history is preserved.