Nested fragments do not work with client-preset and documentMode="string"

[stefanoverna]

Which packages are impacted by your issue?

@graphql-codegen/client-preset

Describe the bug

When using documentMode: "string" with @graphql-codegen/client-preset, in case of nested fragments, only the first level of fragments are included in the final query.

The Github repo reproduces the issue clearly.

Your Example Website or App

https://github.com/stefanoverna/codegen-string-bug

Steps to Reproduce the Bug or Issue

yarn
yarn start

Notice that the output on the page is just:

query Video($id: ID!) {
  video(id: $id) {
    ...DetailsFragment
    __typename
  }
}

fragment DetailsFragment on Video {
  title
  __typename
  ...MovieFragment
  ...EpisodeFragment
}

So, MovieFragment and EpisodeFragment are missing.

Expected behavior

MovieFragment and EpisodeFragment should be part of the query.

Screenshots or Videos

No response

Platform

• OS: macOs
• NodeJS: 16.20.0
• graphql version: 16.6.0
• @graphql-codegen/client-preset version: 3.0.1

Codegen Config File

import { CodegenConfig } from "@graphql-codegen/cli";

const config: CodegenConfig = {
	schema: "schema.graphql",
	documents: ["src/**/*.tsx", "!src/gql/**/*"],
	generates: {
		"./src/gql/": {
			preset: "client",
			plugins: [],
			config: { documentMode: "string" },
			presetConfig: {
				fragmentMasking: { unmaskFunctionName: "getFragmentData" },
			},
		},
	},
};

export default config;

Additional context

No response