Get dot separated deep attribute keys for faceting tag attribute to use with refinements list

End goal here is to use an attribute on the objects called attributes that is an object and make refinements lists with the vue instantsearch component ais-refinements-list

something like

const settingAttributes = [
  'attributes.Thing',
  'attributes.Other thing',
]
<div  v-for="refinementAttr in settingAttributes">
  <ais-refinement-list :attribute="refinementAttr" />
</div>

Problem is to do that I need a list of the dot separated deep attribute keys from the index.
I have the attributes object and it is marked for faceting in settings

Screen Shot 2021-06-22 at 8.54.00 PM

I looked at search

algoliaClient.initIndex(indexName).search('query', {
    attributesToRetrieve: ['*'],
 });

And then switched from algolia lite and pulled settings

import algoliasearch from 'algoliasearch';
export const getSettings = () =>
  algoliaClient.initIndex(indexName).getSettings();

Which returns an object with the keys

{
  attributesForFaceting: [
    "attributes"
    ...
  ]
  ...
}

But how do I get the deep values?