### 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)

int dc = dir_access->get_drive_count();
	if (dc == 0 || access != ACCESS_FILESYSTEM) {
		drives->hide();
	} else {
		drives->clear();
		Node *dp = drives->get_parent();
		if (dp) {
			dp->remove_child(drives);
		}
		dp = dir_access->drives_are_shortcuts() ? shortcuts_container : drives_container;
		dp->add_child(drives);
		drives->show();
		for (int i = 0; i < dir_access->get_drive_count(); i++) {
			drives->add_item(dir_access->get_drive(i));
		}
		if (p_select) {
			drives->select(dir_access->get_current_drive());
		}
	}
}
bool FileDialog::default_show_hidden_files = false;
void FileDialog::_bind_methods() {