Is it idiomatic to say "to increase the quality of code base"? Like for example in the following sentence:
The refactoring increased the quality of the project’s code base.
Yes. That is completely normal, and you will see it in technical documents a fair amount. It's maddeningly non-specific, but entirely expected. If you are going to interviews, be prepared for them to ask in what way it improved the quality. Was it more readable? Less redundant code? More type-safe?
The linguistic reasons that it's fine is that quality is a property that can be increased, and you have specified fully what you increased the quality of. It's not the simplest sentence structure, but it's pretty straightforward.