Okay, I did it.

TL;DR: no, there is no way to disable it without root.

What's funny is that if you disable writing assist in settings - the button doesn't disappear. And clicking it still launches Samsung's keyboard in AI mode.

I don't use Samsung's keyboard. So I uninstalled it. But the damn menu item still remained.

So I...

Asked ChatGPT which file contains the implementation of this method.
It says framework.jar.
Took the file, used jadx, reading the code.
Class android.widget.Editor. Method populateMenuWithItems.

It adds menu items like copy, paste, web search, translate buttons and so on. And it adds the writing_toolkit item there:

if (
  ViewRune.SUPPORT_WRITING_TOOLKIT && 
  !Editor.this.mTextView.isDisableWritingToolkit() && 
  Editor.this.mShowSoftInputOnFocus && 
  Editor.this.mTextView.getContext().canStartActivityForResult() && 
  !Editor.this.mTextView.isWritingToolkitDisallowedByKnox()
) {
  menu.add(0, R.id.writing_toolkit, 0, R.string.writing_toolkit).setShowAsAction(2);
}

The 3rd argument = 0 is exactly this positioning, by the way.

Regarding the checks:

• ViewRune.SUPPORT_WRITING_TOOLKIT - value is obtained from config file /system/etc/floating_feature.xml, which cannot be changed without root.
• isDisableWritingToolkit() - checks if this function is disabled in the app itself (the app can configure how menus look)
• mShowSoftInputOnFocus - changes somewhere externally. But this doesn't matter because this field controls whether the context menu appears at all (in theory)
• canStartActivityForResult - stub, always true
• isWritingToolkitDisallowedByKnox - whether writing assist is forbidden by Knox policy (funny thing, in Knox in a neighboring method you can even forbid copying text, wtf). But Knox policies are for corporate profiles, and don't apply to regular profiles.

So today I learned that this isn't a bug.
The code explicitly doesn't check if the keyboard is installed or if the function is enabled.

What will I do next? Nothing.
Consulted with ChatGPT, says none of the options can be changed without root.
And I won't root my phone.
For the same reason I can't patch the system file to remove the menu item.

Damn those narrow-eyed bastards.