And compilers are effectively a rudimentary form of test. They are not sufficient, nor necessary but they do validate some basic assumptions about the code.
They also remove redundant testing (you only need to prove something fulfills certain properties once as long as you have a type for it); and the more advanced the type system the fewer tests needed.
It's not just about confidence. It's also about the speed you can use/refactor the code. Suggestions, type information on hover and instant feedback if you forgot, used wrong order or type, misspelled or simply don't remember exactly signatures or auto generated documentation means a lot when writing code. You can move much faster when working on typed code. Nobody ever claimed that types are replacement for tests. It just means that your tests don't require obvious clutter anymore, you can focus on more complex/important test cases to cover.
Tests only help if they are written, and if they cover the code in question. Both of things are unfortunately not always given. If things are not covered by tests type systems are still better than nothing.
