There are not as many sysadmin job these days because so many on-prem deployments have moved to the cloud. Consider becoming a cloud version of a sysadmin (whatever they're calling it now...). Every platform offers lots of free learning resources and has a certification process.
What I would do is get a lot of experience with a lot of different systems.
If you're enjoying self hosting and setting stuff up, go to something like TurnKey Linux and download a handful of applications that you're interested in using.
Spin up virtual servers on a proxmox server, install the turnkey Linux systems, and then learn how they work. Get ldap running on your home network. Set up an nginx reverse proxy and get a certificate so that you can go to a duckdns internal name spaces instead of IP addresses.
Find use cases for your home network system and then find how to make the systems you have available work for those use cases.
And for the love of god, find yourself a cheap Windows server license and virtualize one of those and integrate it into the mix.
Host a WordPress or Joomla on IIS, set up a pihole for your home DNS on Ubuntu server.
Run a jellyfin server and download a bunch of public domain movies to it.
Hello, find yourself some Kiwix images that you like and figure out how to get https and nginx names running on them.
The more you play around with the technology, the more you'll find out what you like doing and what you don't like doing and what you're good at and what you're not good at and that will help you understand where you fit and wear your talents lie.
Once you know that I'm sure you can put those talents to use for gainful employment.
Programming is the biggest skill you can learn, as it helps with automation and separates you from install clickers. You don't have to be advanced, just the basics helps troubleshooting when you understand how software flows from the inside.
You list an education qualification in your post which has nothing to do with your stated intention. Yes, you're learned and probably smart but why do you want to be a sysadmin?
Have you ever coded anything? Do you want to learn that? Do you want to use your humanities degree to be a caring supporter of stupid system users? Are you even aware of the credo of the bastard operator from hell?
Sorry...saw your post and just wanted to take a piss...you'll be fine if you want to do that but it's probably not just like "installing linux" on a computer.
Why the rudeness? My post says I enjoy managing my home stuff and am considering it as a backup job opportunity other than my PhD. Nothing unclear there.
Don't mind my jaded fellow IT pro. The job eats at you if you're in a bad position, which I'm guessing he/she/they/drag is.
In a small way I can see they're trying to help (even if the delivery stinks), as IT isn't just something you can dabble in and then pivot into it at this point in time. If you want to work in IT you really have to want it and make it a priority simply because the competition is fierce and getting started is grueling and will potentially burn less dedicated people out.
To support that point it's worth pointing out that the entry level of the industry is both very saturated and generally very unsatisfying help desk work. Without dedicated experience in system administration and/or formal education in IT you're most likely only going to get a help desk position, and that's if you're lucky.
That's not the end of the road though, at that point you'll need to absorb as much knowledge as you can, get some certifications to show you know what you're doing (which certs will definitely change by the time you get there.). Once you have them you can leverage those certifications into a better position. That position might be a junior sysadmin if you're lucky, but in my experience those positions want years of experience in sysadmin tasks.
As the saying goes: The hardest part of getting into IT is getting a helpdesk position, the second hardest part is getting the hell out of helpdesk.
That's the general roadmap. If you have more specific questions feel free to ask away.