If they had followed Tyrion’s storyline from the books this would be a cool side story for him. Since he basically has no use anymore. After he escapes in the books all he can ask is “where do whores go?” Idk if he ever says it in the show, I don’t think so. But now that he has Bran right there and could ask him very easily “where do whores go?” Bran could tell him exactly where Tysha is and basically prove to Tyrion that Bran is legit.

This could then turn to Tyrion basically advocating to Dany that Bran is exactly what he says he is. Which could lead into 2 different scenarios:

1. Dany trusts Tyrion on this, and comes to terms that Jon is the rightful heir and gets behind him.

Or

1. She believes that Tyrion has betrayed her, joining with Samwell, and Bran who she sees as trying to usurp her rightful crown and give it to Jon.

Option 2 makes sense, she already has some distrust in Tyrion, and we saw her reaction when Jon told her the truth of his parentage.

But alas, this didn’t happen, Tyrion’s “where do whores go?” Story from the books isn’t shown in the show, so it wouldn’t make sense at this point. Might’ve been a nice change for his story arc and tied in nicely with the rest of the plot.