or-->but was just playing with his smartphone

or-->but was just on his phone

Not one, but several men, were doing the same. I wondered why they were using their smartphones instead of shopping. Although, looking at them carefully, I realized that they all came with their partners. The women stood next to those men were choosing the items seriously.

^This phrase makes sense but sounds odd. Use a word like actual, or rephrase to emphasise THEY were shopping.

-The women stood next to these men were doing the actual shopping.

-The women stood next to these men were the ones doing the shopping.

The men were bored with shopping

or-->bored of shopping (sounds more natural)

and were on their phones to kill time. I felt it was not too long ago that I often saw a man standing next to a woman, waiting with a tired look, saying "Hey, have you decided? Either one is fine!", but the time has changed!

or-->but the times have changed (sounds more natural)

or-->but how the times have changed! (This is a common phrase)

I was impressed to find that.

or-->I was impressed to discover this. (Better word choice)

Although it seems that women spending a lot of time shopping has not changed. How about in your country?

You have a very good grasp of English, and the story made me laugh. As a guy, I think it's much better nowadays with smarthphones :).

In the UK, "smartphone" is not often used, and sounds unnatural if repeated a lot, so we just say "He's on his phone" or "He's using his phone".

Lykke til med norsk òg!