I have one character that is unable to connect to NGS either through the character select screen or with the block transfer teleporter. They can connect to base PSO2 without issues.
All of my other characters can connect to both NGS and base PSO2 without issues.
When trying to solve this, I had found this thread on the steam discussion forums: https://steamcommunity.com/app/1056640/discussions/0/5079478487783186729/
That thread is for the opposite issue for me, as I cannot access NGS. If the solution is to do the inverse and remove mixed items from my NGS storage, I don't seem to have any way to access that from base PSO2.