Nuke your twitter profile
The time has come where we should not be active on Twitter. The following tools have been helpful for me in blasting away all my tweets.
https://github.com/Lyfhael/DeleteTweets is, if you're not scared of running a bit of javascript, pretty good and seems to work the fastest, although it works best if you're able to provide a file from the backup that twitter generates for you.
And yes you should grab a data export from twitter.
If you're maybe a bit more nervous and have a smaller account, then https://redact.dev/ will do the job with its free options. I'm not sure if the github script unlikes posts but redact does so you may want to use both.
In most of my cases I've found that I've needed to run a couple of times or manually delete half a dozen stragglers. But it works.
You could probably also just deactivate your account, but this way you can maintain your handle to prevent someone else from squatting it. And it IS handy to have an account simply because you may need to see things other people post there, and the logged-out experience is nasty. But after nuking your tweets I'd recommend getting rid of any shortcuts and uninstalling the app so you are not tempted to open it up (if you for whatever reason do need to look at something there on your phone then just do it in a web browser).
Do not go "oh yeah I agree with this, we should get off twitter" and then keep going there and posting and retweeting stuff.