Sub panel grounding conductor "splicing" with main panel grounding conductor at electrode

The feed from the new main panel / meter to the inside sub panel is 4 wire from the main panel. Inside the sub the neutral is isolated from ground. Are you thinking that the sub ground comes directly from the ground electrode? I think this would be a code violation for a new system as 4 wire feeders have been code since 99. Since the sub is in the same building a separate ground electrode is not required and if a grounding electrode conductor is added would create a parallel path.

Now if you want to sink a new grounding electrode at the panel and connect it to the sub that would be code compliant. But your feed from the main is required to be 4 wire and a parallel grounding conductor would violate code.

No, the Equipment Grounding Conductor from the required 4 wire feeder to a 120/240v subpanel must be connected to the ground bus in the panel feeding it.

In all panels fed downstream from the service you will need remove any bonding jumper and separate Grounded Conductors (neutrals) and Equipment Grounding Conductors.

You need to re-connect all grounding electrodes (building steel, metal water piping, encased rebar, pipes, and rods) to the new service, connections need to "continuous" [per 250.64(C)].

The existing grounding electrode connections to the Grounded Conductor (neutral) must be disconnected in sub-panels, those connections could be could be completely removed, but I think you could leave them connected to the ground bus. I could be convinced otherwise, but to me I don't see any difference specified in the code between a panel mounted on building steel that is an electrode, or connections to any other type of electrode.