Both Asana and Jira integrate with a number of leading apps and products across the web. They both will meet your demand with basic needs like integrations to Google Drive or Microsoft Teams. Asana has done a nice job of integrating with most apps of any substantial size that you might want to connect with, and it is easily the best option if you’re looking to integrate pretty widely.
Jira, however, has focused a lot of its integrations on things that product teams will need, like Miro or GitHub. This will exponentially speed up your project management if your purpose is to manage and push out new product features.
One of the interesting things to consider is that Asana and Jira integrate with each other. Your business could, potentially, use both products and let them work together. This could be the right choice if you have large projects that involve more than just a product team, but that team wants to use Jira to streamline their own internal processes.