I found a fix for this issue but nobody is going to like it too much.
Maybe do a backup first. (I rarely do this & have been inconvenienced at time or two.)
Delete the Twitter app. Reset the cache in Safari. Restart.
Then go to “Settings” — “General”. Scroll to the bottom. Tap “Reset.” And then “Reset all settings.”
This will, of course, wipe out all of your settings. It will remove all of the Apple Pay cards that you have set up. It will remove your Apple ID settings as well as your mail settings. You’ll have to redo your Face ID & redo your passcode. *All* settings will reset.
You should not lose photos or notes or any data, such as 1Password info. None of this stuff was disturbed on my iPhone 11 Pro.
After your phone restarts, download Twitter. Enter your info & open it.
Then set up iMessages in settings. Sign into your Apple ID.
In Messages, tap a link for a tweet. It should open in the Twitter app.
If it works, we win.
As I redo my settings, I check after each setting change to see if Twitter will still reopen via Messages. It’s survived everything so far— even switching to dark mode, setting up Face ID, signing into iCloud, setting up mail.
Apparently the links to trigger the opening of the Twitter app via a link broke during an update.
Hopefully Apple will not do this again in the next update, which should be out soon— probably next week.
Please do post if this fix works for you.