If you're in a hurry (or just lazy), just make sure to read the first 15 or so lines!

I'll get into detail later, but to give you an idea let's imagine any single player tournament:
PREPARE A reasonable amount of time prior, the community is informed that there is going to be a tournament. Announced on the forum, discord, in-game etc. Servers are prepared as well.
REGISTER There's a window of, say, 30 minutes before the tournament where people go into discord and sign themselves up through a command with a tournament bot. For example: !register
ORGANIZE Once this window closes, the bot randomizes a suitable bracket and the players start their first match in the server specified by the bot. The bot can start out simple, but sky's the limit when it comes to features (seeds, double elimination etc.)
PLAY As the tournament progresses, there are essentially two ways to handle this: either we (the players) report match scores to the bot through chat commands in discord (I like this), or some person updates the brackets as the tournament progresses (I don't like it because it's less automated and relies on volunteers).
SAVE Once the competition is over, the finalized brackets along with relevant information is saved somewhere, arguably here on the forums.
And to finish off the brief part of this post: no, it's not the same as pickup just because there's a chatbot involved. Some differences being that these are single planned events with a start and a finish and a winner at the end. Pickup games are obviously very different than tournaments. Let's not make this a debate on this vs that. That'd just waste everyone's time.
MORE ARGUMENTS AHEAD. (Good job getting this far. Feel free to stop here and reply with your inital reactions...)
If we do set this up, thus making it very easy to organize some tournaments, it'll be quite important that we don't overdo it. To make sure we organize the right tournaments in moderation, (once we've gone through a testing phase and find the system working), I suggest we use forum polls to decide on intervals and gamemodes. It's also possible to do polls in discord (vote by "reacting"), but as the discord is a closed environment we should encourage forum activity where possible. Otherwise, how are curious visitors going to know that the community isn't dead?
There's no bot yet. I've asked karas (owner of the discord channel) and while he may have the skills to create such a bot, he lacks the time for it. While a mindset of "no worries, someone will make it work" isn't ideal (and not what I'm going for), there's definitely an argument to see if there's a demand before we start working on the supply. That's what this thread is for. If it ends up being well received by the community, there's a much bigger incentive to start working on a bot.
What's wrong with the wiki and google docs? Nothing wrong with those. But it does require a fair amount of manual labour from a small amount of people to make things happen. Ideally, we'd still have the occasional wiki-based tournament. For example if fort tournaments (or any mode with big teams) became a thing again there's no reason not to use the wiki. However, for 1 or 2 player teams, a more streamlined option makes a lot more sense.
Who would be allowed to create tournaments? Anyone? Just a chosen few? Anyone with an idea that passes a poll by some arbitrary percentage? I don't know. While I believe it's important to keep it moderate (more than one tournament per weekend would probably be too much), freedom is pretty nice. As long as we work together, it could go many different (but still good) ways. Since you sign up on the same day, and don't necessarily have to plan ahead to commit, we might discover new things about running successful tournaments. Heck, we might even find out that Tuesday is the best tournament day rather than Sunday. Who knows?
Isn't this going to be stressful for server owners? I mean, without them we'd have no tournaments at all. And every time there's a tournament, somebody needs to create a bunch of server configs and the server owner needs to spend some time on setting them up. But, I think if we go ahead with this system, there are ways to make it require even less work from server owners. If we can create a "base config" and allow a team of admins to go into the server and change game modes as needed, all the server owner has to do is keep the server online (I suggest one main and one backup per VPS; never to be used at the same time though, but literally a backup in case main one breaks) and sometimes update access levels. As long as we can find a team of admins that are both active and trustworthy, I predict that server owners will have to do less work per tournament than before.
Do we need more tourneys? I've noticed a very clear connection between tourneys planned and grid activity. Most of us are competitive, and we wanna win. Winning public games is cool, but winning a tournament is way better. More tournaments is good.
Aren't there tournaments planned already? How will this affect those? There's probably a sumo bar tournament coming up soon, and I've "soft announced" mini-TST 3 for May 10th. These should probably be unaffected by this thread/idea. Just finding a working bot and setting up servers should take a while. And if I know our community at all, this discussion could take some time as well. That's if anyone even joins it.

So yeah, would love to hear what you all think about this.