In InstantSearch version 4 we added federated search. This means that the uiState might have multiple indexes that need to be stored in the URL, so we now include them in the URL by default.
There is more detail on this here: https://www.algolia.com/doc/guides/building-search-ui/upgrade-guides/js/#routing
However, this can be easily removed by specifying the index you are using, for example:
There is also documentation for the routing parameter here: https://www.algolia.com/doc/api-reference/widgets/instantsearch/js/#widget-param-routing
Here is a working Codesandbox example of this: https://codesandbox.io/s/routing-remove-index-name-we8gw?file=/src/app.js
Magento extension only
To make this change within Magento 2 you will need to change the search options to include this routing change: https://www.algolia.com/doc/integration/magento-2/customize/instant-search-page/?client=php#change-search-options