### 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)

} else {
				ti->set_icon(0, theme_cache.file);
			}
			ti->set_icon_modulate(0, theme_cache.file_icon_color);
			if (mode == FILE_MODE_OPEN_DIR) {
				ti->set_custom_color(0, theme_cache.file_disabled_color);
				ti->set_selectable(0, false);
			}
			Dictionary d;
			d["name"] = files.front()->get();
			d["dir"] = false;
			ti->set_metadata(0, d);
			if (file->get_text() == files.front()->get() || match_str == files.front()->get()) {
				ti->select(0);
			}
		}
		files.pop_front();
	}
	if (mode != FILE_MODE_SAVE_FILE) {
		
		if (tree->get_root() && tree->get_root()->get_first_child() && tree->get_selected() == nullptr) {
			tree->get_root()->get_first_child()->select(0);
		}
	}
}
void FileDialog::_filter_selected(int) {
	update_file_name();
	update_file_list();
}
void FileDialog::update_filters() {