How would you improve the Starbucks app?

I would start by getting to understand the objective of the improvement. Is it to improve revenue or engagement.

Lets say it is to improve revenue. Then looking at the personas who use Starbucks app frequently, I would call out 3 – Busy office folks, Travelers and Coffee Connessiurs

Picking up one of the personas, lets say busy office folks, their customer journey has the following painpoints
1. Finding the store closest to them with min preparation time
2. Easy parking spots
3. Knowing coffee is ready

Focusing on their biggest pain point, i.e.” Finding the store closest to them with min preparation time”, we can start with a few solutions.

1. Display a map of nearby stores with total time to reach+ the time to get the order ready in the selected shop based on traffic data and queue in each store.

2. Automatically choose the best store for the customer depending on total time at each store, giving an option of changing the store if required.

3. Give an option of prioritizing their order in the nearest store by paying higher for the coffee in peak times.

Choosing the best solution based on impact to revenue, ease of implementation and customer wow, I would go with solution 3.