I'm afraid the split view has a limited function different than what you want. It allows you to view different parts of the same screen. That's it.

Here's an old article that covers the issue. From there:

Let's start with View -> Split View, which is a source of confusion
because the split is a clone, not an independent window.

The purpose of this is to give two views of the same document or
whatever output you are monitoring. For example, suppose you are
studying a long configuration file. The split view shows the same
document in both panes, but you can scroll independently to bring up
different sections of the document side-by-side.

As far as konsole goes, you'll need to open a new window and arrange them to meet your needs. You could resize them and drag the windows to position them the way you want or use kwin shortcut to, for example, "snap" the windows to occupy half your machine's screen using Super+Left and Super+Right.

The workaround, is first to open a new tab, and then use split view. Work in one tab in one view and work in another tab in the other view. They'll be independent. You can use Shift+Tab to switch between tabs.

Using tabs and split view:

And here's a reddit thread on using Yakuake which splits screens the way you want.