refactor: split regular and existence join in hash join

### Is your feature request related to a problem or challenge?

Regular joins (inner/left/right/full) and existence joins (anti/semi/mark) are different relational operations; separating them can potentially make them simpler and easier to maintain.

The following issue describes the why. I believe it's a different problem, but with exactly the same core philosophy, and it provides a more detailed writeup.
- https://github.com/apache/datafusion/issues/22710

### Describe the solution you'd like

_No response_

### Describe alternatives you've considered

_No response_

### Additional context

_No response_