How can I provide input field arguments with apollo federation 2?

Question

I am trying to federate two of my micro services with apollo gql federation 2. I have successfully connected the two services through the federation with the following schemas:

Subgraph1 - Product

type Product @key(fields: "id") {
    id: ID!
    title: String!
    description: String
    price: Int!
    category: [Category!]
  }

type Category @key(fields: "id") {
    id: ID!
  }

type Query {
    product(id: ID!): Product
  }

Subgraph 2 - Category

type Category @key(fields: "id") {
    id: ID!
    title: String
  }

and the following query

query Product($productId: ID!) {
  product(id: $productId) {
    id
    title
    category {
      id
      title
    }
  }
}

gives a desired result

However, what if I wanted to add some filter on the returned categories for a given product. Lets say I only wanted to have the ones with title "sport", so the query would look like this instead:

query Product($productId: ID!) {
  product(id: $productId) {
    id
    title
    category(searchTerm: "sport") {
      id
      title
    }
  }
}

A normal way of doing the input argument would be simply just

type Product @key(fields: "id") {
    id: ID!
    title: String!
    description: String
    price: Int!
    category(searchTerm: String): [Category!]
  }

Is this achievable when federating the services? I am not sure how the input field is provided to the second subgraph?

I tried to add the input as a part of the type in the first subgraph, however it does not seem to pass the search term to the next graph.