Using Google Trends diagram in a scientific paper to show evidence of interest in an area

Yes, you can use it, but treat it like any other source of data.

I have been encouraged to use Google Trends data as supporting evidence by my professors. You would need to explain the implications of the data, including caveats, just like any other type of data. In the case of Google Trends, be careful not to overstate what it is saying. It is only counting searches made on the Google platform, so what does this tell you directly, and what does it imply indirectly?