Work/Products gets "finished" - Projects get "finalized"
Finalized is not a synonym "finished" with different connotations. The words refer to related but distinct things.
For example, consider a project to create a software application:
The developers do their work, until they are "finished."
Then various other defined tasks within the project are done (testing, user acceptance, management sign-off, etc.). When all the required steps are complete, the project is "finalized."
Then imagine a serious flaw is discovered. It is clear that there is work to be done - the product is not "finished." But the project has been "finalized" - that does not change. (And the work to fix the flaw will probably be part of a new project.)
finalize
is also a function/method in some languages (e.g., Java) that indicates an object is no longer in use. It's possible that it might have crept into wider usage by technical folk due to that.