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I think the stamps in your link will cut into the surface rather than make an imprint - this may not be a problem if the leather is dyed through (iron salts and tannin?) but may be an issue if the black is a surface finish not unlike paint.
I don't see why traditional pyrography wouldn't work, relying on a change in texture rather than colour. Branding and laser engraving both work with leather - just be aware of the smell if done indoors!
I've only ever used that type of stamp on metals - challenging to get the characters in line, and even more to achieve an even depth, giving a functional marking than anything aesthetic! The only time I have made a decorative leather stamp was a one-off using a CNC engraved acrylic stamp and a press, applied to wet leather for an hour or so - not conventional, but sufficient to customize MrsE's phone case.
You might get a better answer in the Crafts thread:
https://www.lfgss.com/conversations/178272/
MrE-
I definitely second the bit about lining up the characters being a challenge - it's a frikkin' nightmare. Achieving an even depth is easier - at least it is if you are stamping aluminium.
I punch a dimple into the blunt end of the stamp. Then, using an automatic centre punch, place the pointy end of the automatic centre punch into the dimple, and it isn't difficult to achieve a consistent depth of punch. Not sure that an ACP has enough grunt in the spring to achieve the same on steel.
JurekB
I would like to make a small inscription on a couple of black leather belts.
Are these my best bet?
https://www.amazon.co.uk/AmazonBasics-Metal-Leather-Stamp-Kit/dp/B0783J7PFM/ref=asc_df_B0783J7PFM/
Does pyrography work on black leather?