Bracketing Discord's downsides, it is in many ways very polished and able to support many users. Fluxer attempts to exactly clone Discord's user experience. The story behind Fluxer contains a lot of interesting technical details and is worth reading. But to summarize, Discord is closed source and (in addition to a bunch of other stuff) uses Elixir and React, whereas Fluxer is open source with an AGPL-3.0 license and (in addition to a bunch of other stuff) uses Erlang/React. But hey, Gleam can do a lot of what Erlang/Elixir do with OTP and what TypeScript does on the client, right? So couldn't you write a Discord clone mostly in Gleam without compromising on the tool fitting the job?
Because the Fluxer guy has done a lot of great work reverse engineering Discord, and because users looking for alternatives to Discord are probably motivated by free and open software, I think you'd want to copy Fluxer and its license.
A basic chat app is, uh, basic, like you could probably do one in the tutorial for [whatever language], or even an AI could poop one out. At the same time, there are tons of painstaking details for user preferences and performance. So a Discord clone is an interesting project for an afternoon or a decade.
I also feel like it would be good for Gleam for people to make more applications, as opposed to more libraries. Ideally libraries are pulled out of common application work, rather than created because they sound cool. So more applications means better motivated libraries. And a Discord clone would really test what Gleam can and can't do in terms of OTP and Lustre.
I really want to focus on fhir and not get sucked in to some rabbit hole, otherwise I'd try myself. So if you like Gleam and are looking for something to do, try a Discord clone!