The Run box is safe, although not useful for multi-line content. That tweet (now deleted) was referring to the Start menu search box.
“You are correct. This traffic was not generated by typing text into the "run box", it was generated by typing text into the "start menu box". We are very sorry for the confusion this has caused.”
I’ve always got BBEdit open and a quick New file from clipboard command creates the document. I can either recopy that or do some adjustment and then recopy. It’s a little more effort than using the browser address bar, but I can more easily see and fix problems.
Now I use Notepad or Ctrl+Shift+v.
One advantage to using Notepad is that it reveals newlines in your paste data very clearly, so you can select a substring if needed.