### 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 (search_text->get_text().is_empty() || results_count == -1) {
		matches_label->hide();
	} else {
		matches_label->show();
		matches_label->add_theme_color_override("font_color", results_count > 0 ? get_theme_color(SNAME("font_color"), SNAME("Label")) : get_theme_color(SNAME("error_color"), SNAME("Editor")));
		if (results_count == 0) {
			matches_label->set_text("No match");
		} else if (results_count_to_current == -1) {
			matches_label->set_text(vformat(TTRN("%d match", "%d matches", results_count), results_count));
		} else {
			matches_label->set_text(vformat(TTRN("%d of %d match", "%d of %d matches", results_count), results_count_to_current, results_count));
		}
	}
}
bool FindReplaceBar::search_current() {
	flags = 0;
	if (is_whole_words()) {
		flags |= TextEdit::SEARCH_WHOLE_WORDS;
	}
	if (is_case_sensitive()) {
		flags |= TextEdit::SEARCH_MATCH_CASE;
	}
	int line, col;
	_get_search_from(line, col);
	return _search(flags, line, col);
}
bool FindReplaceBar::search_prev() {