Overview
This is a memo on performing case-insensitive search when using Drupal’s Search API.
Method
Access the following page and check “Ignore case.”
/admin/config/search/search-api/index/<content_type>/processors

Furthermore, in the Processor settings at the bottom of the screen, select the fields to which you want to apply this processing. It was also possible to select all fields as shown below.

By performing reindexing, the above settings will be reflected.
Summary
I hope this serves as a helpful reference.