WD external hard drive software

I recently purchased a WD HDD external hard drive with built in time machine software.

Not quite - the backup software on a WD drive is for Windows only. It's called WD Backup. See here: WD Backup is a Windows only software for WD DAS (Direct Attached Storage). It is recommended using the built-in utility from Apple for backing up a macOS computer.

Time Machine software is part of macOS and is engaged when you mount an external drive on your Mac. See Back up your Mac with Time Machine.

However I find some people on the net recommend erasing this and reformatting the drive

Not just recommended - you will need to format it because the WD drive is pre-formatted for Windows. See Erase and reformat a storage device in Disk Utility on Mac using APFS file system.

Also was thinking to partition. How much should I keep for back ups of my 1TB mac?

All of your drive should be reserved for your Time Machine backups.

FYI, it is best to partition & format every new drive so you know the partition layout and file system are compatible with your computer and are using the latest version of the file system layout in order to take advantage of current features. You never know for sure what the manufacturer put on the drive or if the layout & file system are outdated as was mentioned by someone in this thread. Even if you intend to use the seemingly same file system. I do this just to be safe. Plus back when I used Windows, it was a way to make sure something nefarious wasn't hidden on the drive which could have damaged by Windows installation.

As far as using NTFS which is usually the file system of choice for the majority of external drive manufacturers, I highly recommend using Disk Utility to erase the whole physical drive in order to use a built-in macOS file system which is less likely to break after a macOS update/upgrade. A recent macOS security update did break the third party NTFS drivers back in March, and as far as I know none of the third party NTFS drivers have been updated yet since users are still complaining about not being able to access their NTFS volumes.

If you need to share a drive with both macOS & Windows, then it would be best to use Disk Utility to erase the physical drive as GUID partition and exFAT. If you intend to only use the drive with macOS, then erase the physical drive as GUID partition and MacOS Extended (Journaled).

Quite so. I was forgetting about some of these. I have an iMac and use the powered drives which I've always found to be reliable, but in NTFS, at least those I researched.

Regardless, note that the My Passport seem to be formatted in the old HFS+ Journaled format rather than the post-macOS 10.13 APFS, which is okay but not the current standard. Ultimately it seems not to matter much for backups, and some experienced Community members recommend HFS over APFS.

Regarding the use of the drive, the chief reason for exclusive use is that over time your backups will consume an increasing amount of space. Time Machine is designed to accumulate your backups. If you use it for other purposes it shortens the span of time available within the backups. I guess too that the more use a drive gets the shorter is its life, and all drives have a finite lifetime. Then there will be the issue of accessing your data on a Time Machine drive and competing with the backup regime to use the drive simultaneously. The backups happen frequently - every hour - and in the background so that you are unaware of it happening. Access at this time would be slow and I wouldn't want to potentially compromise a backup. Given you have a notebook this is something you could control a bit more than we desktop users by mounting, backing up, then dismounting, so that might not be a factor unless you intend to leave the drive plugged in for extended periods. My powered Time Machine drive is always mounted and running, though asleep until it's called upon to leap into action.

I also like to segregate and unify my data on drives rather than mix and match.

The acid test though is how much value you place on your Mac's data. Is it worth it to you to make the small outlay to get an external just for the purpose of Time Machine backups?

Format and manage the drive with Disk Utility. Do not use the third party included software. Let the MacOS manage the drive.