I run a company focused around Shopify store acquisitions, and I'd like to create a process through which sellers come to my website, give be their API credentials, and authorize me to pull their performance data from their shopify site.
I know that this is possible- as a number of my competitors do so.
Can someone please advise as to how I can extract the data when given the API key?
You can use the Shopify Analytics API: https://shopify.dev/docs/admin-api/rest/reference/analytics.
That allows you to programmatically generate reports similar to what you can do inside the Shopify admin. It's a bit restrictive (store needs to be on Shopify Advanced), so another tactic you can use (if they authorize it) is to tap the Shopify Order API to get order data for the last 30 days, then use some math on your server to get average order value, total sales, etc.