The custom share menu lets you send tweets to a selection of recent contacts via direct messages, and you can add content to your bookmarks or copy a link to a tweet. When you want to use another app, you need to tap the "Share Tweet via..." entry.
One of the new implementations retains all of the old options in an extra row, including a shortcut to the system share sheet, but it adds another row with direct sharing options to other apps.
From twitter support page " Share Tweets even faster. Now testing on iOS: when you tap the share icon on a Tweet, your top apps will be on the “Share Tweet” menu for easy access."
By default, the "Share via" shortcut is hidden at the end of the vertically scrolling list, but as soon as you tap it, it takes one of the first spots — the share targets are sorted by engagement.