I've deleted my Twitter DMs (inspired by @LisaForteUK), here's how to do it real easy ...
1) Request a download of your complete Twitter archive. You do this from twitter.com/settings/account under "Privacy and Security" -> "Download archive with all your data".
2) Wait for your email stating your data is ready. It took 3 days for mine to arrive. Download it when it's ready.
3) Head over to semiphemeral.com/ which is run by @micahflee (doing this requires that you trust him, as technically he is going to be able to read your DMs, so consider whether you do or not - blog post about all of it here micahflee.com/2020/09/semiphem…)
4) Authoritze Twitter for the app, this happens automatically
5) Head to "Settings" and authorize the app to access your DMs
6) Switch to the DMs tab, and upload the data/direct-messages.js file into the web interface
7) Wait a while, check the "Dashboard" page every once in a while
That's it ... you can nuke your Tweets and Likes the same way.
This probably doesn't do any difference to the Twitter backend storage *actually* deleting them, YMMV.