The situation with regard to an employer/employee is that the IP belongs to the employer if the design is employed unless there is any agreement to the contrary. If the design is an outside contractor or self employed, then the design is the IP of the designer unless there is an agreement to the contrary.
In this situation therefore as there appears to be no agreement to the contrary as to who owns the IP of any design which they have done for you) then the IP belongs to them.
From what you say, although your contract with the public art people say that you own the copyright, that is only between you and them and is nothing to do with you on the manufacturer. It appears to be an oversight on your part that you didn’t come to an agreement with the manufacture as to who would only IP.
They do not own the IP if anything was made by them but from your design. They only own it from anything which they designed.
They appear to have tried to impose their terms and conditions by sending them to you after the event.
Unless you have dealt with this company over a regular and persistent course of dealings, they cannot rely on terms and conditions given to you after the event. Hence, they are of no effect.
Nonetheless, what I have said in the first paragraphs with regard to the ownership of IP, still applies.
The simple (without going into individual features) test as to whether you have reached their IP would be whether a private individual would look at the new design and the old design and conclude of that the new design was actually the old design but modified.
I’m not certain whether that answers the question for you because you haven’t asked any specific questions but I would be happy to answer any specific questions which arise from this. Kind regards