first time sending my package

so I sent my switch lite from California to Arizona for a service I paid on Etsy. Everything went smooth. But I kept thinking about when they asked me if the package had batteries in it. And I replied that I was not shipping batteries and that I was shipping a Nintendo switch lite. (powered off, and packaged with care) but then I remembered that the switch lite has a battery in it😭 I looked around the internet and saw that I should be fine because the lithium contents and weight are far less then the parameters , plus the battery is installed and not ship by itself. I just wanted to see what you guys think and what I should do or just relax