The ticket def. needs to be reissued (i.e. the ticket will be updated and gets a new ticket No.) and only TK is able to do that. Currently, the flights in Feb 2023 do not match the ticket in the reservation and you will not be able to travel. UA only changed the flights in the reservation but will not be able to/will refuse to reissue award ticket issued by another airline.

You need to contact your local TK ticket office and explain that UA has rebooked/changed the flights and ask TK to reissue the ticket. Hopefully, TK will not object to the fact that the new travel dates exceed the validity of the ticket, but give it a try. But give it a few days; it's possible that UA has requested TK to reissue the ticket (it can take a while to get reissued), but if the ticket No. remains the same as originally issued last year, you need to take action.