### 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)

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	} else {
		int idx = filter->get_selected();
		if (filters.size() > 1) {
			idx--;
		}
		if (idx >= 0 && idx < filters.size()) {
			String f = filters[idx].get_slice(";", 0);
			for (int j = 0; j < f.get_slice_count(","); j++) {
				patterns.push_back(f.get_slice(",", j).strip_edges());
			}
		}
	}
	String base_dir = dir_access->get_current_dir();
	while (!files.is_empty()) {
		bool match = patterns.is_empty();
		String match_str;
		for (const String &E : patterns) {
			if (files.front()->get().matchn(E)) {
				match_str = E;
				match = true;
				break;
			}
		}
		if (match) {
			TreeItem *ti = tree->create_item(root);
			ti->set_text(0, files.front()->get());
			if (get_icon_func) {
				Ref<Texture2D> icon = get_icon_func(base_dir.path_join(files.front()->get()));
				ti->set_icon(0, icon);