Extend Hydra search context to generate filter fields client side?

Question

I'm using API Platform 3.1. When you've got an entity with a ApiFilter, Hydra will give some information about all fields with a filter. In this simple example it will give the name of the field (createdAt):

class Entity
{
  #[ApiFilter(DateFilter::class, properties: ['createdAt'])]
  protected ?DateTimeInterface $createdAt = null;
}

'hydra:search': { 
  "@type": "hydra:IriTemplate"
  "hydra:mapping": {
    "@type": "IriTemplateMapping",
    "variable": "createdAt[after]",
    "property": "createdAt",
    "required": false
  }
}

This information can be used to populate search fields client side, like Swagger does:

Now I want this information to generate a form with fields that can be used to sort or filter. But I want not only the field names, but some extra information about how the filter can be used. For example: a date field createdAt should render a slightly different datepicker than a birthdate field.

I've already tried extending the Hydra context as described in API Platform's documentation:

#[ApiResource(operations: [
    new Get(hydraContext: ['foo' => 'bar'])
])

But I didn't found foo/bar in my /api/items response.

Is there a way to add some information to the Hydra model which I can use in my application?