How to update the URL of an Android TWA?

So Our PWA already handles push notifications that tell it to go to a new URL. I got the TWA up and running and the push notifications are working except they don't do anything, they just open the app. I can get the data in the notification using

Intent appLinkIntent = getIntent();
String appLinkAction = appLinkIntent.getAction();
Uri appLinkData = appLinkIntent.getData();

What I can't find is how do I tell the TWA to go to the new URL after it's already started? Can you not update the URL of a TWA?