What are these weird spoons we have and what are they for? [SOLVED]

I believe what you have there is an ice cream spoon. Thinner on one side to aid 'slicing' through the ice cream.

A search for "asymmetrical spoon" gives a few that are shaped just like OP's. These ones look particularly close in shape. They also have sort of similar design around the handled ends - at least in that they have designs rather than a fully plain end.

OP doesn't say anything about the flatter side being thinner or sharper. I think if meant to cut into grapefruit or ice cream that side would be sharper/thinner. Absent sharpening, a pointy spoon should penetrate something easier than a less pointy one - and these look less pointy than if they were symmetrical. Plus, you'd bend those up pretty quick in hard ice cream I think. I think they're just asymmetrical for the sake of it, a point of distinction perhaps marketed as favoring right handed people in getting liquids off a flat surface better.

I think it's a pudding spoon.

The slightly pointed tip is to aid slicing the pudding, while being assymetrical to allow a right handed person to not get the pointy end pokies.

It's for grapefruit. https://www.amazon.com/Pieces-Stainless-Steel-Grapefruit-Serrated/dp/B01N92I6V0

There are various tooth edged spoons with the various amounts of teeth that are designed for grapefruit some have more teeth some have less but it's designed to separate the meat from the skin and pull it out of the halved grapefruit leaving the dividers in place so that you get some nice juicy grapefruit instead of chewy segment skin.

Makes me kinda think it's a french sauce spoon, but it's still missing some key features. Flat edges are meant to scoop sauces easier from plates etc..

Doesn't look exactly right, but maybe a quenelle spoon?