Well I think he has the blue lightsaber to show how he was tooling with Kylo given that Kylo just destroyed that lightsaber the scene before and didn’t even notice it due to how angry he was.
That might be part of it, but I don’t think there’s really any question that it’s a symbolic thing. Rey offering Luke the lightsaber is an explicitly symbolic gesture, we know she’s not just gifting him his lightsaber back, she’s asking him to come back and ignite that “spark of hope.” She does it twice, and both times he refuses. When he does come back to “ignite the spark,” it only makes sense for him to have the lightsaber Rey offered him.