Is H-1B stamping needed?

Hi, I have unexpired H-1B visa stamp on my passport. Recently extension got approved and I am planning to go to India. Can I travel back with the current visa stamp (+current and extension approval notices) or do I need to go for stamping in India ?

You can travel and enter back as long as the visa is valid on the day you enter. Yes you can use your extension I-797 while entering back so that the CBP will issue I-94 to match with your extension expiry.