How can I link users across multiple subdomains?

I am trying to create a website that would contain 2-3 subdomains. The reason I want it to include subdomains is because the website is split up into several distinct parts, and each part requires its own theme and plugins.

Is there some way I can have users register for one site, and either 1) be automatically registered for the other subdomains or, preferably, 2) link their accounts to share names/info when they create an account on another subdomain?

The ideal would be to have something that operates exactly like SE, just on WordPress. When you create an account on a new SE site, it automatically syncs up your account with your existing one. That’s what I want.

How can I achieve this result?

A plugin would be extremely desirable, but is not necessary.

The fact that you haven’t mentioned MultiSite in your post makes me think that doing some research there would be a good next step for you:

https://codex.wordpress.org/Create_A_Network

User Accounts are shared across sites in the network, and sites can be different subdomains.