Nah.
Edo itself is when Shogonate began to decline. a slow decline.
and just 'Shogunate' lasts for an entirety of Age II. 'From beginning to Madatory end'. This covers both Viceroy Hojo Tokumune (he didn't use title 'Shogun', back then no one uses this title yet, and it was also the time consonant kana 'n' (ん, ン) didn't invented yet..)
I’m not a Japanese historian by any means, so feel free to correct me, but my understanding is that this claim basically would assume that the shogunate was one continuous thing.
I’m pretty certain that’s an incorrect understanding of Japanese history—the shogunate was an office which was occupied for 800 years or so, across multiple periods (Kamakura, Muromachi, Azuchi-Momoyama, Edo)—of which 250 were under the Edo Period. The Shogunate didn’t decline across the totality of the Edo period, it only declined towards the end of it, and the early to mid Tokugawa shogunate represented a time of stability.
obviously towards the 1800s, the Tokugawa shogunate began to struggle, but that would make sense and even fit the thematic structure of the eras (since that would be towards the time of the Meiji restoration, and Meiji Japan is a Era III civ already)
The Shogunate was an office, but no more so than say, the emperor of China. You wouldn’t call all of China “Imperial China” or say that the Qing don’t deserve to be marked as a civ because it was the period where the emperor’s office declined. Japanese periods are more like the periods of China/India where the only things that are common is the fact that there was a shogun—and even this wasn’t always true in those 800 years. The Edo period is also arguably where the shogun was the strongest as an individual.
Decline is often a part of eras, but just because an era did decline doesn’t mean that the whole era is undeserving of recognition for its notable accomplishments.
think there's a slight possibility they could just go for the name Shogunate Japan, if they wanted to encompass attributes all of them, and then make Antiquity Japan everything pre-shogun. But if they do go for a specific one than Edo Japan does make the most sense
the only reason i doubt they will is because they chose Meiji Japan over a generic Japan. They could pick Heian or Kamakura Japan, but I think Heian period Japan thematically is more appropriate for Antiquity despite its time scale (by Khmer logic), and Edo Period Japan is more compelling than Kamakura Japan, though I wouldn’t have complaints either way.