No? It appears that neither you or the Twitter poster understand what you're reading.

The "increased vehicle storage space" is in the sense that there will no longer be traffic waiting to head to 11th sitting in the queue at the Jersey Ave light.

If 25% of cars were going to 11th before, building a new exit taking them off the road before there means there's now 25% more queue space leading to the the Jersey Ave light.

The net result of this is that traffic into Newport/that region of JC would be far less impeded by the Holland Tunnel backups. As you are presumably aware, 11th St is intentionally configured to make it impractical to use to try to cheat the Holland Tunnel queues and that wouldn't be changing.

The purpose of the Turnpike's Extension's expansion is for increasing traffic demands on the NJ side from both the port/industry and general population growth on the east side of the bay, not for somehow increasing Holland Tunnel throughput.

I'm not endorsing the plan, to be clear. But your criticism isn't at all about the problem they're claiming to be doing this for or fixing.