### 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)

filter->clear();
	if (filters.size() > 1) {
		String all_filters;
		const int max_filters = 5;
		for (int i = 0; i < MIN(max_filters, filters.size()); i++) {
			String flt = filters[i].get_slice(";", 0).strip_edges();
			if (i > 0) {
				all_filters += ", ";
			}
			all_filters += flt;
		}
		if (max_filters < filters.size()) {
			all_filters += ", ...";
		}
		filter->add_item(RTR("All Recognized") + " (" + all_filters + ")");
	}
	for (int i = 0; i < filters.size(); i++) {
		String flt = filters[i].get_slice(";", 0).strip_edges();
		String desc = filters[i].get_slice(";", 1).strip_edges();
		if (desc.length()) {
			filter->add_item(String(tr(desc)) + " (" + flt + ")");
		} else {
			filter->add_item("(" + flt + ")");
		}
	}
	filter->add_item(RTR("All Files") + " (*)");
}
void FileDialog::clear_filters() {