The piece in question is called 'Atomic Galaxy wall-hanging sculpture', an original artwork by C Jeré that was recently auctioned. You can see the signature in the closeup.
It might interest you to note that it was displayed (in the show) upside-down.
Their work can be found in several of the crew's quarters. As a matter of interest, professional Star Trek memorabilia collector zredthunder was offered the piece prior to the set auction but declined it due to its size and expense.
That is 100% a Jere’ piece of wall art. I had the opportunity to
purchase the original when I bought one of the three Datas room marble
based pieces with the chrome ball at the top also made by C. Jere’.
You can see an earlier piece with a similar style (by the same artists) below.