Your flight can be confirmed but not ticketed. As well as above advice go to Finnair Manage Booking and email your receipt (repeat for all pax). You will receive a full itinerary including seat res, Fare Class and Fare Basis and a Receipt showing Name, Ticket Number, Form of Payment, Fare, Fare Equivalent, Taxes, Issuing Airline and Date, Restrictions/Endorsements and Fare Calculation. It's more comprehensive than BA and is similat to the old style paper tickets from eons ago. Fare Class is the revenue class booked in eg J,C,D,R,I in Business and U in Business redemption. Fare Basis should start with the same letter as fare class but if not you may have been booked into a higher fare class in the same cabin e.g. if no redemption seats available when you need to rebook a cancellation.

Check the Issuing Airline and date to make sure it is on or after the date you changed your flights.

BA may have sent you a Confirmation of Changes email or an e-ticket receipt email with the same 125-xxxxxxxxxx ticket number. You should also see this in the BA App.

Form of Payment may refer to a card number or say XXX-Paid which seems to tie back to a previous ticket somehow. Mine says CAX Paid and all my ticket numbers align so I'm happy even though I get the Error message when trying to print e-ticket in BA MMB.