I can only tell you what worked for me. It’s not a sim card solution. I put my Indian sim card in an iPhone which was left in India and all my other Apple devices were set to receive iMessage. And my OTPs came in almost real time on my Macbook and iPad. My mom charged the iPhone SE 1st gen once every 2 days. It worked flawlessly for years. I recharged the connection in time to avoid any disconnection. However, FaceTime doesn’t work this way, so you won’t get your Mac to ring in the USA when your phone is in India.
i know now Android have a messages.google.com/web portal so it should work with your Android phone as well as long as you don’t lose cookies and get signed off and your messaging app on the Android phone is Google’s own messaging app. Other Android specific solution is TeamViewer (or Anydesk) to your Android phone. This is what I did before iMessage solution.