Prior to the NEXT update, I had a base with all the Specialists and (I think) all the recipes. Then NEXT happened and when I got back in my base had been bundled up to be unpacked later. Fine.

I flew around, found a place to set up house, and unpacked my base. Everything was there *except* for my Specialists. Their workstations were there, but they were no where to be seen. I went to a space station...no Specialists to rehire. I did an E on the terminals back in the base and was told (essentially) "You need an <x-type> specialist which you can hire on a space station." I went back to the station. Nope.

I used the teleporter and teleport to stations that said, "Potental Overseer Recruit"....no one there to hire. I thought perhaps I needed to jump start things by rebuilding their stations, so I dismantled them, then rebuilt them. Still no Specialists.

I have no Specialists and none seem to exist.

Then I discovered that (probably because I have no Specialists) I also lost a lot of my recipes! I can't make glass any more because I don't have the recipe and I don't have a Specialist to teach it to me.

How do I get them back?

I think you can just "activate" the stations after you rebuild them by clicking Use on the workstations which makes the NPC's spawn in

All the specialists I had on my pre-NEXT freighter base were still there after the update. I had a plethora of other things going wrong, but didn't loose my specialists. I even had recipies for things new NEXT players seem to no longer be able to obtain, ie the Standing Planter, if I remember correctly.

I've since started new saves, and didn't load my pre-NEXT one for quite a while now.

Which version of NEXT have you tried ? A new patchlevel (1.57) has just become available. Maybe that's worth trying, doing a clean install and then copying your old save back.