While I was researching the early 1900s Go players all across Japan, I found this very interesting list
Notice the people circled in red
Inukai Tsuyoshi (犬養 毅) and Toyama Mitsuru (頭山 満), the first one Inukai Tsuyoshi was a cabinet minister at the time, and later Prime Minister of Japan (where his death by assassination indirectly lead to the progress of War World II in East Asia), and the second one Toyama Mitsuru was a key player in East Asia “spy network”, where every event regarding Korea, China, and Japan between the 1890s to WW2 had something to do with him.
Although it was not uncommon for nobles, businessmen, and industrialists to sponsor Go since the 1870s (after the Shogunate failed, and Go communities looking for new financiers), and list them as guests or honorary members, while these sponsors themselves are usually novices. But I actually found a game played by Toyama Mitsuru against 吉田俊男 (Yoshida Toshio, son of 吉田半十郎 5 dan - a founding member of Hoensha, and Toshio said to have the strength of at least Shodan)
I transcribed it below to correct an error
From the look of it, Toyama Mitsuru was a pretty strong player himself, not just a simple sponsor. There is even a picture of him playing a 13x13 game with Inukai Tsuyoshi
From all the information I found, there was something fundamentally changed during the 1890s to 1910s in the Go community in Japan, and most likely the real root of amateur Go community started to emerge.