You can move a Drupal site from Search API Solr to the Opensolr Search module while the old search keeps working. The two modules do not depend on each other, so both stay installed until you switch.
01 · Steps
Install Opensolr Search
composer require drupal/opensolr_search, then enable it. It needs no Search API. Installation.
Connect a new index
On the Settings tab, save your Opensolr email and API key, then choose Create a new index. Use a new index rather than the one Search API Solr writes to: the module puts its own Opensolr configuration on the index it uses. Connect your account.
Fill it
Start the Data Crawler, or run Ingest All Now on the Data Ingestion tab: which one to use.
Rebuild your facets
Search API field settings do not carry over. Map the fields you filter on in the Facet Mapping tab, index again, and turn them on in Facet Configuration: examples.
Check the new search page
Try your usual searches at /opensolr-search, then adjust Search Tuning, Elevation and Filters.
Switch
Once an index is connected and the search page is on, Drupal's core Search block and its /search page already send visitors to /opensolr-search. Search pages you built with Views keep their addresses: redirect them to /opensolr-search or change your links.
Remove the old setup
When you are happy, delete the Search API index and server and uninstall the modules you no longer need. The Opensolr Index that Search API Solr used stays in your account until you delete it.
02 · Before you start
What changes, side by side: Opensolr Search and Search API Solr. The whole module: Complete Guide to the Opensolr Search Drupal Module.