All I've been able to find is cmd + K O, which opens the active file in another window. Searching for a keyboard shortcut to open the active file in a new tab in a split window.
I want to start with one tab open with index.js, and end up with two tabs, each with index.js, ideally in a split window.
The keybinding command IDs you are looking for are the ones that start with the prefix workbench.action.splitEditor. You can open your keyboard settings file with the Preferences: Open Keyboard Shortcuts (JSON) command, or open the keyboard shortcut editor GUI with the Preferences: Open Keyboard Shortcuts command.
To learn more about how to customize keybindings, see https://code.visualstudio.com/docs/getstarted/keybindings.