Hello Sultan! It can mean both, but is more commonly used as "adding some lures to motivate/attract people to make or do something" here in the United States. In the example you mentioned above ("This may provide the right nudge"), it is definitely referring to the meaning of "adding some lures to motivate/attract people to make or do something". More often than not, you would say "He pushed him" or "He shoved him" rather than "He nudged him" when talking about physically pushing someone. Hope this helps!

It's mostly your 2nd interpretation. It means providing just sufficient motivation that it will make a difference.