Maybe if you count the post-Sorkin years
As a part of "The West Wing
that we got", which is what I was talking about, yeah, I'd count shows that aired as a part of the original run. But go back and look at the early seasons, too. For example, Josh is absolutely essential to the second-season opener, as who really got hurt in the shooting, who got Sam on board, who accepted Donna. It's really only in the middle episodes of the original run, including the latter part of the Sorkin run, that the focus shifts heavily onto the Bartlets, and even then, Josh and Donna still matter a great deal to the plots.
That's a very poor analogy
Any analogy between Star Trek
and The West Wing
becomes a poor one, as soon as chain of command is taken into consideration, because there is no analog for TWW staff in Federation starship crews that we are ever made aware of; maybe we'd be talking about something like a bunch of captain's yeomen.
The main WW characters like Leo, Josh, CJ, Toby, and Sam were the senior staff, the department heads, just as the main TNG characters were the senior staff.
Josh was Deputy
Chief of Staff, under Leo, until season six when he went to the Santos campaign, and Sam was Deputy
Communications Director, under Toby, until he resigned in season four. As Press Secretary, CJ's immediate boss was also Toby, until she became Chief of Staff in season six.