### Godot version

v4.1.stable.official [970459615]

### System information

Windows 10

### Issue description

When changing the `file_mode` of `FileDialog` from "Open File" to "Save File" via code the "Save" button keeps disabled until a file or folder is selected if the "Open" button was disabled before.

Basically the button activity has to be updated when `file_mode` is changed. I have made the change already but the last time I opened an PR without an issue some people requested I open one. So here you are!

### Steps to reproduce

- Open the MRP and start it
- click anywere to open the dialog
- after 10 seconds the dialog changes file_mode
- if the button is disabled before the change it is as well after it

### Minimal reproduction project

[file_dialogue_test.zip](https://github.com/godotengine/godot/files/11991311/file_dialogue_test.zip)

makedialog->popup_centered(Size2(250, 80));
	makedirname->grab_focus();
}
void FileDialog::_select_drive(int p_idx) {
	String d = drives->get_item_text(p_idx);
	_change_dir(d);
	file->set_text("");
	_push_history();
}
void FileDialog::_change_dir(const String &p_new_dir) {
	if (root_prefix.is_empty()) {
		dir_access->change_dir(p_new_dir);
	} else {
		String old_dir = dir_access->get_current_dir();
		dir_access->change_dir(p_new_dir);
		if (!dir_access->get_current_dir(false).begins_with(root_prefix)) {
			dir_access->change_dir(old_dir);
			return;
		}
	}
	invalidate();
	update_dir();
}
void FileDialog::_update_drives(bool p_select) {