but since some of these domains have been around in my GSC for months now, I'm wondering... Is there any way a website could "conceal" the links when visited manually, but "show" them to google? If so, why would they do that?
Your site has been hacked.
What someone has done was installed a script and/or modified server configuration files so that when the server detects Google's IP address and/or a user agent string that matches a device only Google would use, the page that is loaded is your HTML modified to include the links to the spammy-looking domains. It's possible the modified HTML replaced your links with the links to the spammy-looking domains. This would affect Google only in this case, but the hackers could affect any search engine.
Sad news if you're not fluent with programming is that there is no easy way out.
The lay mans way out is to download all your own website content to your own computer and remove any unwanted configuration in the HTML files, then reset the server (meaning have the administrator reinstall the web server software and delete all garbage), then once the server is clean of viruses and such, test your domain to make sure everything works, then re-upload your files, and if applicable, reinstall your Content Management System.
Now if you have some sort of server experience, then look in server configuration files for anything that clues you in on google pointing to modified content. If your web server software is apache, look for any rewrite rules or the like that show google or its ip address as a parameter and remove them.
Another idea is (provided you have programming experience) to look in the script files themselves if you have any. In Wordpress, your script files end in .php. Look through each of them and remove added lines that show google or its ip address.
Its hard to specifically pinpoint which lines in particular in each script or configuration file to remove because hackers can hack in different ways, but hopefully you'll get a start.
Another thing you might want to look at are your server log files to see if google is being redirected to the modified pages. It's possible the hacker made that happen as well.