Clear safari cache. Delete twitter app. Restart iPhone. Settings—General—Reset—Reset All Settings.
NOTE; This will reset ALL settings to default. Apple Pay will need to be redone, as well as ALL tweaks and passwords. Data will not be touched— like 1Password, notes, calendar, contacts= OK after reset of all settings.
Before doing this, know the passwords you will need for your WiFi, Apple ID, etc.
After your device finishes resetting, select WiFi. Insert password. Download Twitter app. Sign in. Open iMessages. Sign in. Test a link from iMessages to Twitter app.
This works on iPhone 11 Pro. So far, it has NOT worked on iPad Pro 12.9”.
iOS 13.1.2 created issue. Then Twitter updated their app which caused the issue to return. Then IOS 13.1.3 AGAIN caused the issue to rerun.
If this fix works for you, maybe turn off auto-update for awhile until Apple gets this sorted out because redoing all settings every other day or two is a royal pain.