There are plenty of reasons to get rid of most of your social media, I do think that the fediverse (Mastodon, Gnu Social, etc) are in general a good option, but less and less the commercial networks.

Tweeting is becoming a non compensating activity. For most of us, that we do not had much followers, twitter is becoming a high risk activity. There is trolling, there is the risk of decontextualisation, employers might not like your tweets, advertisers would profile you with ease... tons of fake followers, ANGER, and so on. It's just not worth it.

So, when you delete your twitter, a very important thing to take into account is the SEO and how do you appear on the search engines. In order to deindex yourself, first thing to do would be to make your account private. That will slowly deindex your timeline. However answers from other public timelines citing your handle will still appear and will be indexed. When people search your handle this will come up. So after having our account made private we should change our handle.

When you go with a browser and you are logged in a javascript will resolve to your new handle, while it won't be updated on the timelines. So, what you need to do next is to register a new twitter account with your now free, old handle. Twitter will start resolving to this new profile instead.

I would leave this for 1 month, then deletion is OK. Another good option is to use a tool to delete your old tweets and let the search engines index this, then delete.

As afterword, I would say that is hard to follow certain things, events without twitter. So I keep an account. A new one, always private and no followers (so that you can't see who I'm following). Also this account never does likes. And probably the most important, really reduce and filter, remove all the upsetting accounts. Those accounts perhaps leave it for private list if you still interested.

And better move to mastodon for healthier microblogging and increased control.