What are examples of large Arduino code bases and how are they organized?
Big projects are likely not developed with Arduino IDE. Arduino IDE was make for designers/inventors, not for programmers. 


  Arduino was born at the Ivrea Interaction Design Institute as an easy tool for fast prototyping, aimed at students without a background in electronics and programming. 


Source

Programmers will use a fully-fledged IDE which has many features a programmer needs on a daily basis, such as:


handling multiple files efficiently
allowing to create libraries instead of just setup() and loop()
code completion (suggestions as you type)
debugging (inspection and changing of variables at runtime)
refactoring (modifying the structure of your code without changing the behavior)
integrated version control (like Git / Github)


Such an IDE could be Eclipse with an Arduino Plugin or Atmel Studio and perhaps Visual Studio.

So, what do you need to look for? Don't look for .ino files. Instead, look for .h and .cpp code, just like other non-Arduino C++ code. 

Some examples:


SPI: 297 lines
Wire: 453 lines
SoftwareSerial: 486 lines
I2S: 533 lines
USBHost: several files, up to 1600 lines