As others have said, the easy change is going from a 6 speed to a 7 speed freewheel.

You’ll need to know your current freewheel. If the smallest cog is 14t and the largest is 28t. Then going to 13-34 freewheel will give you a little bit higher end and about 20% lower gearing for climbing. You might have to get a 14-34 if the 13-34 can’t be found. Don’t get a Megarange where the jump is 24 to 34.

I saw a BTwin Hoptown model with a Tourney rear derailleur. Depending on the exact model, I think it will handle a max cog of 34t. This is important because you only need the freewheel and a 7 speed shifter, and most likely a new cable.

The main difference between a 7 speed “freewheel” and a 9 speed “cassette” will be 11t and an another extra cog; and a lot of cost. You’ll still be limited to 34t for climbing.

John