Best file system for external hard drive backup on Mac mini M4

NTFS is about the worst option you could use. It's the native Windows format and, by default, NTFS volumes are read-only on MacOS, which makes it a really poor choice for backups :)

The only format you should consider is APFS. This is the most flexible and supports all current OS versions, formats and idiosyncrasies (encryption, case-sensitivity, resizing) etc.

Types of disks you can use with Time Machine on Mac - Apple Support

APFS is currently the preferred format for Time Machine backup direct to external drives, whether HDD or

SSD.

Backup speed is really irrelevant beyond that first big copy task, so any performance hit a HDD might take with that format may be ignored.

You do not say what kind of external drive you will be using; a SSD or a rotational HDD? APFS is designed for SSDs and can be hard on HDDs, particularly cheaper HDDs which often use SMR technology.

https://eshop.macsales.com/blog/43043-using-apfs-on-hdds-and-why-you-might-not-want-to/

https://support.bombich.com/hc/en-us/articles/20686495048215-Choosing-a-backup-drive#recommendations

SSDs are fast but are more expensive, particularly large ones. Personally having a fast backup drive doesn't really make much difference to my setup. Yes, the first backup takes a long time, but later ones are much faster.

Then also comes the question about using Time Machine (TM), or an alternative backup utility such as CarbonCopyCloner or SuperDuper. TM will want to format any new drive to APFS but there may be a way to avoid that if you are planning on using a HDD.

I personally went with a 6TB CMR HDD on a docking station. I have to finish setting it up but I plan on trying to have TM use a HFS+ formatted partition.

APFS is optimized for SSD, taking advantage of the features of SSDs, while overcoming some of the shortcomings, in ways that HFS+ (the predecessor to APFS) never did because it was developed way before SSDs became mainstream.

That's not to say APFS won't work for HDDs. There may be cases where HFS+ outperforms APFS on HDDs, but it's likely to be not significant if your primary goal is backup. The article you reference hints at this - for read-write intensive tasks, HFS+ on an HDD may be better than APFS, but for backups and mostly-static data, this is a moot point.

The OP didn't specifically say they were using Time Machine for backups.

I agree that HFS+ is preferred for Time Machine, due to the way it stores historical copies of data, but there are many other forms of backup. Maybe clarification from the OP is in order.