Just to make it more compact, instead of posting every single log, how about posting one message, then edit it according to current status?
I'm talking about the discord api, think it's possible to edit the message (https://discord.com/developers/docs/resources/channel#edit-message), so when it's down, the message would change red and show the needed stuff, then when it's back up it'd change to green and show that, and perhaps some info on the last downtime?
This way we would have one message in the server status channel, always showing the current state.
If someone wanna check out a detailed log, you could put a link there in the message itself.
Since we have two web servers now, perhaps show two messages, one for the game and one for the beta?