### 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->insert_text_at_caret(repl_text, 0);
				if (match_to.x == selection_end.x) {
					selection_end.y += repl_text.length() - search_text_len;
				}
			} else {
				
				text_editor->insert_text_at_caret(repl_text, 0);
			}
			rc++;
		} while (search_next());
	}
	text_editor->end_complex_operation();
	replace_all_mode = false;
	
	text_editor->set_caret_line(orig_cursor.x, false, true, 0, 0);
	text_editor->set_caret_column(orig_cursor.y, true, 0);
	if (selection_enabled) {
		
		text_editor->select(selection_begin.x, selection_begin.y, selection_end.x, selection_end.y, 0);
	}
	text_editor->set_v_scroll(vsval);
	matches_label->add_theme_color_override("font_color", rc > 0 ? get_theme_color(SNAME("font_color"), SNAME("Label")) : get_theme_color(SNAME("error_color"), SNAME("Editor")));
	matches_label->set_text(vformat(TTR("%d replaced."), rc));
	text_editor->call_deferred(SNAME("connect"), "text_changed", callable_mp(this, &FindReplaceBar::_editor_text_changed));
	results_count = -1;
	results_count_to_current = -1;
	needs_to_count_results = true;
}
void FindReplaceBar::_get_search_from(int &r_line, int &r_col, bool p_is_searching_next) {