Get Payment Method from order


I want to receive the transaction_id of the current payment method I’m using.
Currently I’ve some trouble achieving this.

What I have so far $order->getTransitionLogsJoinProcess()->getFirst(); which returns BraintreePayPal01.
But how can I get an instance of my current PaymentMethod to access the transaction_id ?
My order is of type SpySalesOrder

In the documentation I cannot find anything for that.

thanks for hints