### 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
replace_text->select_all();
			replace_text->set_caret_column(replace_text->get_text().length());
		} else {
			search_text->select_all();
			search_text->set_caret_column(search_text->get_text().length());
		}
		results_count = -1;
		results_count_to_current = -1;
		needs_to_count_results = true;
		_update_results_count();
		_update_matches_label();
	}
}
void FindReplaceBar::popup_search(bool p_show_only) {
	replace_text->hide();
	hbc_button_replace->hide();
	hbc_option_replace->hide();
	selection_only->set_pressed(false);
	_show_search(false, p_show_only);
}
void FindReplaceBar::popup_replace() {
	if (!replace_text->is_visible_in_tree()) {
		replace_text->show();
		hbc_button_replace->show();
		hbc_option_replace->show();
	}
	selection_only->set_pressed((text_editor->has_selection(0) && text_editor->get_selection_from_line(0) < text_editor->get_selection_to_line(0)));
	_show_search(is_visible() || text_editor->has_selection(0));
}
void FindReplaceBar::_search_options_changed(bool p_pressed) {