My experience with flights operated by Finnair has often been 7 day posting of TP after the flight (although in one case it did not post for me and I had to fill in the online form which I don’t think can be done until 14 days).
After posting you probably have to wait another 24-48 hours for your new tier to activate.
Until at least the TP show in the app, there is little chance to use the new benefits (even then you have to ask nicely to use lounge etc), and in most cases you will need to wait to the new tier level to fully flow through.
Sorry, probably not the best news for your current trip! But I am sure you will enjoy next time
