I had $7K worth of tickets that I booked back in February for a trip starting on 5/2 (refundable biz fare FWIW). Finnair cancelled the flights and I waited until I got an email from them informing me that the flight has been cancelled. I got the email the last week of March and filed a refund request online on 3/28 or 3/29. I received a confirmation email shortly after informing me that the refund will take up to 8 weeks to be processed and if I prefer to receive a travel voucher with a 10% bonus that will be processed within four weeks. We chose to continue with the cash refund. On 5/12 the refund posted to my AMEX.

The Finnair FAQs indicates that refund is taking 8-10 weeks so give them time and avoid doing chargebacks if possible unless the airline explicitly refuses to provide a refund like AF/KLM.