According to the Salesforce documentation1, reporting performance can be affected by various factors, such as the volume and complexity of data, the design and configuration of reports and dashboards, the number and type of users accessing the reports, etc. To improve reporting performance, some of the recommended solutions are:
Move data off of the platform and run reporting outside Salesforce, and give access to reports (option C). This means using an external service or tool that can extract, transform, and load (ETL) data from Salesforce to another system or database, such as a data warehouse or a business intelligence platform.
This can improve reporting performance by reducing the load and latency on Salesforce, and enabling faster and more flexible reporting and analysis on the external system. Users can access the reports from the external system using a link or an embedded component in Salesforce.
Contact Salesforce support to enable skinny table for cases (option B). This means requesting Salesforce to create a custom table that contains a subset of fields from the Case object that are frequently used or queried. A skinny table can improve reporting performance by avoiding joins between standard and custom fields, omitting soft-deleted records, and leveraging indexes on the fields2.
Create a custom object to store aggregate data and run reports (option A). This means creating a custom object that contains summary or calculated data from the Case object, such as counts, sums, averages, etc. A custom object can improve reporting performance by reducing the number of records and fields that need to be queried and displayed.
Build reports using custom Lightning components (option D). This means creating custom components that use Lightning Web Components or Aura Components frameworks to display report data in Salesforce. A custom component can improve reporting performance by using client-side caching, pagination, lazy loading, or other techniques to optimize data rendering and interaction.

Virtualizing the remaining set of data with salesforce connect and external objects is the best way to meet the requirements with minimal effort, as it allows salesforce to access data stored in Heroku Postgres without storing it in salesforce. This reduces the storage limitations and avoids data duplication. Heroku connect can bi-directionally sync data between systems, but it requires more configuration and maintenance. Making callouts to Heroku Postgres and persisting the data in salesforce may not be feasible for 1 billion records. Migrating the data to big objects may incur additional costs and require custom code to use async SOQL