The whole idea behind weathering steel is that it will form a very stable rust layer, thus protecting the rest of the material from further rust. So it is usually used in places where verdant is part of the design.
They should last quite a long time without any further treatment.
If you don’t want to rust, that’s the traditional way. Paint, oil, zinc plating, enamel
Or I think you can get them the copper green you want, and then paint them with a low gloss clear varnish.