Not so much bootstrap other communications... but I remember how many penis emblems I encountered on Mario Kart DS despite Nintendo banning them very rapidly.
Nintendo hasn't done a draw-your-own-emblem since, I don't think.
In Splatoon you can "post" [1] which displays this image above your character in the lobby and the main hub of the game. Most of the time people will draw using the in-game interface and the touch screen/buttons on the switch, other times people use a well known exploit to recreate images from your computer in the game using a specific type of controller [2].
After the post is created, it typically gets published to some social media account you have linked to your Nintendo account.
These posts are usually jokes, memes, or some silly throwaway pop culture line or reference but more often than not you see individuals promoting their own discord servers, twitter accounts, twitch accounts, and other social media platforms. Unfortunately you also get a few individuals who will post about LGBT related stuff, often with a sexual angle to it. No issues posting that on Twitter but I feel it's inappropriate for what is essentially a game for children.
The good news is you can report these posts to Nintendo, the bad news is I have no idea if they are moderated or not.
[1] https://thenerdstash.com/how-to-draw-art-posts-in-splatoon-3...
[2] https://github.com/WyseNynja/Splatoon-2-Drawing/blob/master/...
Have people found creative ways to communicate, or solicit/"bootstrap" further communications?
If you can send someone a bit, you have enough to send them your endpoint at another service to communicate. In a multiplayer game, where presumably you can see the decisions of other players, the prerequisites are met.
(I am by no means a gamer, but have witnessed how creative young humans can be at defeating the restraints imposed upon them --- and also how they can quickly learn such things from others.)