Can't change cursor style inside input based on isMenuOpen

[kaua-melo]

Here's what I'm trying to achieve.
1- When menu is not open, the cursor when hovering over the input field (blue area) should be "pointer":

2- When menu is open, the cursor when hovering over the input field (blue area) should be "text":

Here's a codesandbox with my attempt: https://codesandbox.io/s/react-select-v2-custom-styles-forked-rh6z87?file=/src/index.js

I know I could use cursor: state.isMenuOpen ? "text" : "pointer" inside control, but that would apply for the whole dropdown area. I would like to have it applied only on the blue area, where the user types.

Would that be possible with react-select? Or I can only set the cursor based on the state (open/closed) of the dropdown for the whole dropdown (control) ?

Thank you very much in advance!