With a girl only able to use a Senryuu board along with a few other classmates that come with their quirks, they represent as almost any kind of Discord community in existence.
They are depicted as outsiders from everyone else in school as they have odd personalities: Nanako unable to speak but uses a poem board, Eiji with his loud and menacing personality, and Kino only able to express emotions through her sketchbook.
All three of these characters specifically use a non-traditional form of communication like Discord does for people to talk with each other.
Both Discord servers and the Literature Club in the anime bring communities together without using traditional means.
The Literature Club at their school acts as a place the main characters are able to get together in as well as exploring both poetry and drawing as ways to connect with each other.
This club functions just like a Discord server in which few words can be enough at times to have a conversation with other individuals in a chatroom as a Senryuu board doesn't require too many words for Nanako.
Most of the characters within the club, of course, are able to talk verbally as if using the voice chat feature of Discord while, metaphorically speaking, having Nanako talk through a #voicechat channel so she can partake in all conversations they have together.
All in all, Nanako is the sole symbol of people not able to openly speak with others due to shyness but comfortable enough to communicate online. Even if one is too nervous to use a voice channel, anyone is welcomed to communicate through #voicechats.
As for Kino, she represents as artists that use social media like Discord to show their art or as people that use emojis as a form of communication; often reacting to what's said in chat.
Artists are able to have their very own channels on servers in order to have somewhere to express their creations. The club room proves as an excellent place for Kino to be herself unlike anywhere else at school.
As said before, she uses her sketchbook in order to display what she's feeling towards others as she's unable to form emotions on her face.
Lots of people on Discord use emojis to represent how their day has been or to react to something said in chat. For example, if someone says something funny, then one individual may react with an emote that represents them laughing.
And of course, there are other social media sites such as Twitter that apply to this as well. Often times, people online may even react with memes instead of emojis to convey their reactions to something posted.