Any question answered...

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/

@Skülly might be able to help

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?

Not sure (amazon is something I avoid, some others don’t), I bought two lettering sets for saddle stuff from a supplier in the north-east, it’s called LePrevo. Here’s their tool page, I bought the T35 and T31 sets.

If you happen to be in London I’d be happy to lend them btw. Due to forum protocol beer or bike parts must be exchanged, or a donation to the forum itself. I don’t make the rules guv.