The real world equivalent of this timeline is the 1860’s-1880’s when Hokkaido was first colonized by the Japanese properly. There will be traditional buildings and outfits, but also a very heavy European/American influence on architecture as this is what Hokkaido is most known for today in Japan. (Ex: Old Chateau) The professor is said to have travelled to many different regions in order to discover things just as Meiji Restoration Era Japan sent scholars around the world to copy aspects of culture. This is where he got the starter pokemon. Also the town is said to have people from around the world like how early Sapporo had Americans in their universities helping.

Tldr; Lucas’ hat makes sense maybe more sense for this time because people wore hats more in the past. Also don’t be surprised at relatively advanced industrial technology