Seat blocking happens closer to flight time, and you would not see it in on the BA app or website - the “blocked” seat would show as simply available to you, and occupied to others....

expertflyer can actually show you specifically blocked seats

this tends to kick in the day or two before flight, and can change right up until departure - I had a blocked seat showing last month which did turn out empty, but then one last week which reverted to being occupied about 12 hours before flight time - have a blocked seat showing again tonight so let’s see...