How to change the Subscription plan for third party app purchased through iTunes?
With Apple subscriptions, you can either cancel them and let the balance play out or if it just renewed, sometimes you can undo the payment. 

Apple took the money, so cancel with them. When that is sorted and you are outside the coverage of your last subscription, you will have a chance to start a new subscription type. There is no “change” lanes in my experience when one app has different tiers of subscriptions. 



Assuming you cancelled, perhaps there is a period when it’s still active so a chat with Apple support about your specific purchase would be the next escalation if needed. My guess is linked in might only sell basic outside the store, so they might not want to say that directly. I don’t see the words Basic, but maybe the metadata is too long to easily navigate from the in app purchase summary page.