It depends on which version of SDI you're talking about, there were numerous proposed architectures using different technologies, updated through the years as technology changed. In several of the proposals, orbital Boost Surveillance and Tracking Systems (BSTS) would communicate with orbital interceptors using inter-satellite laser links. Brilliant Pebbles particularly called for thousands of orbital interceptors with IR sensors to track missiles, but to arrange an intercept in time a Pebble would need to receive track information from the BSTS, or other pebbles. The challenge of doing that with thousands of pebbles was one of the factors that sank the proposal (the other big problem being the difficulty of actually launching thousands of interceptors into LEO.)

The mesh network aspect of NDSA / Starlink is new insofar as they've now figured out how to do what they wanted to do back then.

Space-based interceptors are missing from NDSA as it's described in public. But all the technical challenges have been resolved, what remains is the political challenge. Since the space-based interceptors are the politically contentious part, if they were going to do this it would make sense for them to build the 'benign' parts first while not talking about the rest.