This feature (twitter DM search bar) has already been added to iOS Twitter devices two years ago, and now it is rolling out to Android users. Ability to filter your messages to find what you are looking for.
The company is finally rolling out a DM search bar to Android devices today after it made its appearance on iOS nearly two years ago. The feature is going to drastically expand how helpful that bar is by surfacing older conversations and even actual words you’ve typed in those conversations sometime “later this year.
The feature which has long been a top request for android users first entered into testing two years ago before rolling out to iOS users.
At the time of writing, it doesn’t let you search the content of messages; you have to type in the names of people or groups. Meaning you can only search for the names of the people you’ve spoken to.
However, if you want to search for your old tweet on desktop, you can use this: https://twitter.com/search?q=YOURSEARCHQUERY%20(from%3AYOURTWITTERNAME)&src=typed_query
This will be a nice feature on mobile too.