The react-google-maps library does not include the Place Autocomplete service; it only offers SearchBox which doesn't allow you to specify fields. However I've done a quick search and have found the following reactjs libraries (and I'm sure there are a few more out there):
react-google-autocomplete which states the following in its readme:
You can also set fields prop if you need extra information, now it
defaults to basic data in order to control expenses.
react-places-autocomplete which doesn't currently support fields as per this issue.
react-google-places-autocomplete which based on the documentation doesn't appear to support specifying fields either.
Note that you can always file a FR or submit a PR yourself.
My approach: take a look at this codesandbox to see an Autocomplete input in action using #1 that only requests Basic Data fields. Add your own API key to the Google Maps JS API script in index.html to run it.
Hope this helps!