Media outlets will foam over for a couple weeks for sure. Facebook will light up brighter.
1. I use Tweetbot instead of the native client. A lot of people gripe about the native client and ads, and using a third party client solves both (ack that this can change, too, at any point).
2. I use Twitter as an RSS feed only, not using it for anything social at all. I only consume updates for feeds I care about, so it’s not very noisy and not at all toxic (unless I go into the comments, which I rarely do).
Sometimes the community makes a successful hop on to somewhere else. Sometimes it doesn't (ie: Tumblr after the Verizon takeover).
Honestly, I wouldn't sweat it. It sucks for the Twitter moderator team / engineers, you know the people who made this their life work. But for us users? We can just pickup wherever the community goes and follow them to the new webpage. Its the life of a digital nomad: we "live" on the internet for free, we don't pay hosting costs and often are bad neighbors / cause all sorts of trouble as a community. Eventually our hosts get tired of us and kick us out, and we gotta find new hosts.
Sometimes, the Digital Nomad spends the money / funds / resources needed to startup a new community (ie: NeoGAF -> ResetEra, or FreeNode -> Libera Chat), and the party gets started very quickly. Twitter was a bit more sophisticated than a simple forum though, but if it truly were a "useful" tool, a replacement tool will come out over the next few weeks/months.
Mastodon is of course the most popular OSS tool being discussed. But who knows what the future holds? Maybe we all go back to blogs and RSS feeds, maybe USENET posts to talk to each other. Or go back to Wikis, and just gotta "be nice" and not erase other people's messages ya know? (Back when we used Wikis as shared communication, if anyone remembers the early days). Neocities looks fine (a nice callback to older web-rings / geocities style pages), and so forth. Plenty of options, its just a matter of waiting to see where the crowd moves right now.
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Right now, before Twitter gets shutdown, is the time to be experimenting with new web pages and connecting with your community. If you _REALLY_ want your community to stick together, message them, "build lifeboats" (ex: Temporary Discord channel or Facebook groups or Email lists), so that you can call everyone back up. When the community figures out where to go (maybe a good ol' dumb phpBB forum), you announce it to your lifeboat and help coordinate everyone you cared about to the new online home.
Twitter didn't "make" the content. People did. Actors, artists, scientists, etc. etc. Those people still exist, they'll continue to exist after Twitter shuts down, and chances are, those people will continue to want to have an online presence somewhere. Its just a matter of figuring out and coordinating the masses to the new location, wherever it may be.
EDIT: If people really wanted an $8/month thingy, then maybe VPS servers with easy-to-use IndieWeb tools would work. We can do anything we want.