### 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
text_editor->remove_secondary_carets();
	String text = get_search_text();
	Point2i pos = text_editor->search(text, p_flags, p_from_line, p_from_col);
	if (pos.x != -1) {
		if (!preserve_cursor && !is_selection_only()) {
			text_editor->unfold_line(pos.y);
			text_editor->set_caret_line(pos.y, false);
			text_editor->set_caret_column(pos.x + text.length(), false);
			text_editor->center_viewport_to_caret(0);
			text_editor->select(pos.y, pos.x, pos.y, pos.x + text.length());
			line_col_changed_for_result = true;
		}
		text_editor->set_search_text(text);
		text_editor->set_search_flags(p_flags);
		result_line = pos.y;
		result_col = pos.x;
		_update_results_count();
	} else {
		results_count = 0;
		result_line = -1;
		result_col = -1;
		text_editor->set_search_text("");
		text_editor->set_search_flags(p_flags);
	}
	_update_matches_label();
	return pos.x != -1;
}
void FindReplaceBar::_replace() {