When Elena Parisi, an engineer, left Italy at age 22 to pursue a career in London five years ago, she joined the vast ranks of talented Italians escaping a sluggish job market and lack of opportunities at home to find work abroad.

But in the past year, as the coronavirus pandemic forced employees around the world to work from home, Ms. Parisi, like many of her compatriots, seized on the opportunity to really go home, to Italy.