### 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)

}
		}
		emit_signal(SNAME("dir_selected"), path);
		hide();
	}
	if (mode == FILE_MODE_SAVE_FILE) {
		bool valid = false;
		if (filter->get_selected() == filter->get_item_count() - 1) {
			valid = true; 
		} else if (filters.size() > 1 && filter->get_selected() == 0) {
			
			for (int i = 0; i < filters.size(); i++) {
				String flt = filters[i].get_slice(";", 0);
				for (int j = 0; j < flt.get_slice_count(","); j++) {
					String str = flt.get_slice(",", j).strip_edges();
					if (f.match(str)) {
						valid = true;
						break;
					}
				}
				if (valid) {
					break;
				}
			}
		} else {
			int idx = filter->get_selected();
			if (filters.size() > 1) {
				idx--;
			}
			if (idx >= 0 && idx < filters.size()) {