The search_api_solr module manages its dependencies and class loader via composer. So if you simply downloaded this module from drupal.org you have to delete it and install it again via composer!
Simply change into the Drupal directory and use composer to install search_api_solr:
cd $DRUPAL
composer require drupal/search_api_solr
This module provides an implementation of the Search API which uses an Apache Solr search server for indexing and searching. Before enabling or using this mod