What is required to unlock the Green Cities DLC climate research station?

The description isn’t clear, but any Industry DLC farm buildings and fields do not count toward the requirements. You would actually need 5000 tiles of zoned farming specialization! It seems you already have 607 of the 5000 farming squares requirement, so you should already have designated farming districts.

Just as a refresher for others who might see this answer, you can designate farming districts by accessing the districts tab, painting a district over an area you wish to be farmland, and designating that district as farming industry. Farms should start popping up and growing, and you should see the squares count requirements go up!