I would like the ability to split the terminal vertically and horizontally with keyboard shortcuts.

Not just a sinhgle split. It may have a limit but it should work the following way:

You hit let's say Ctrl+H and it splits horizontally. You then hit Ctrl+H or Ctrl+V in the active one and it splits horizontally or vertically respectively.

So let's say you hit Ctrl+H three times and then Ctrl+V once, you should end up with the terminal split in three with each part with the same width, the first two with the same height and the third one split in two witch each of those parts having the same width as one another and as the first two parts, height wise they should be equal to another another and vollectively have the height of the first two terminals.

Obviously, we should have key shortcuts to switch between those parts. It can be as simple as just having two shortcuts to switch to next spliy part and previous split part.