### Godot version

v4.0.beta14.official

### System information

Windows 11 22H2

### Issue description

There's not much to it, simply noticed that if you have Find or Find+Replace opened in the Script Editor, the Multi-Caret functionality seems to stop working -- forcibly removing all other carets after the first character is typed. I'd expect the Multi-Caret to remain until unselected by clicking elsewhere.

The content of what's in "Find" doesn't matter, it happens regardless.

https://user-images.githubusercontent.com/8159582/214234069-cbcc1681-3f09-4b10-9a90-857cc91d41a7.mp4



### Steps to reproduce

1. Open the Find or Find+Replace tool in the Script Editor _(nothing has to be inputted)_
2. Add multiple mouse cursors with Ctrl+Alt+Click **OR** highlight something and then highlight additional duplicates with Ctrl+D _(or synonymous keyboard shortcuts depending on OS)_.
3. Start typing as if going to add or replace in all locations where the multi-caret is

### Minimal reproduction project

N/A
if (selection_only->is_pressed() && text_editor->has_selection(0)) {
		_replace_all();
		_hide_bar();
	} else if (Input::get_singleton()->is_key_pressed(Key::SHIFT)) {
		_replace();
		search_prev();
	} else {
		_replace();
	}
}
String FindReplaceBar::get_search_text() const {
	return search_text->get_text();
}
String FindReplaceBar::get_replace_text() const {
	return replace_text->get_text();
}
bool FindReplaceBar::is_case_sensitive() const {
	return case_sensitive->is_pressed();
}
bool FindReplaceBar::is_whole_words() const {
	return whole_words->is_pressed();
}
bool FindReplaceBar::is_selection_only() const {
	return selection_only->is_pressed();
}
void FindReplaceBar::set_error(const String &p_label) {