I'm playing the latest version (8/23/21) on steam and for the first time I picked Edo Japanese. The Shoguns' authority legacy trait reads "+1 influence per population on city or outpost". I have two cities with about thirty pop each and when the turned ticked over I noticed little difference in my influence. I reloaded to check my influence from the previous turn and I had indeed gained no benefit. When I see where my influence is coming from it does not mention the Shogun's Authority trait only that my influence id coming from districts and world wonders.