I have been creating a site for a national nonprofit. So far, everything is going accordingly. However, the administrator recently gave me a demand for a membership only area to publicize some studies, analysis and related content to select audiences. Basically, what I would need is a login area, be it on its separate page or inside an existing one, approval for the accounts created and the ability to display a page linking to these studies in their posts. There is no need for payment or donations of any kind.
My problem is that most plugins I have seen don't offer these capabilities on the free tier, and most plans really do not translate anywhere near realistic price ranges in my local currency. What are your recommendations of free (or at least very cheap, under $100) plugins for that capabilities?

Ultimate Member has a free tier that creates a login and user account pages. You can edit the account page to show posts that are member exclusive. I just installed the plugin myself for a website I’m working on and think it’ll work for your use case. Shoot me a dm if you have any questions!
PaidMemberShipsPro should allow you to create what you are trying to achieve. You can even set different memberhship levels and restrict content based upon the levels.
You can do this with JetEngine if you are looking to build most of it out yourself.
I did something very similar to this using it a few weeks ago. Works well. Just a bit of learning to get your head around it all.
Not free but pretty cheap for what it does.