The system will need to manage a large volume of data—over 1,000,000 records

To be honest that can sounds like a big amount of data but that isn't any problem for a database. It is important to have indexes that are useful for your queries.

Database Design: Are there specific techniques or structures I should follow to optimize the database for scalability and performance? What indexing strategies work best for tables with millions of rows? How should I handle relationships for entities like customers, shipments, drivers, warehouses, etc.?

Start with normalizing your data (I think you can search on database normalization if you do not know what it is)

In the basic run an explain for your query to see if your indexes are used.

And be strict about the used datatypes. By example don't use a text field if you know that you only get a short text in that column.

Performance Optimization: How to ensure queries remain efficient as the data scales? Should I consider database partitioning or sharding in MySQL?

I advice only do this if needed, it adds more complexity to your system

Other Considerations: Any potential pitfalls I should watch out for when designing such a system? Suggestions for handling reporting and analytics without affecting the performance of the main application. I’m open to any advice, resources, or examples you can share. Thanks in advance for helping me build a robust and efficient system!

My basic advice is: do not overthink your database. Normalize your data, think about the indexes and test the performance with a realistic amount of data. If your application grows more then suspected you always have the option to use specific more complex options. But if you start with difficult options it is more difficult to scale down.

And besides that, enjoy you learning with all the options that you can do with your database :)