The easiest way to do this would be to write a custom script to pull the data that you want to display from the osTicket database and display it.
Integrating the product with your other sites/products is really up to you.
As a side note I did something similar here:
https://tmib.net/add-a-client-side-open-ticket-list-to-osticket-1-10/
The article is a little dated, but I still use the mod on one of my production sites. You would need to of course modif it to connect to your osTicket database and pull the information that you want.