When I shutdown my computer last night, it gave me this error message. It seems to be working fine but should I be considered?

Attempting to kill init means that something tried to kill PID 1. That's... abnormal outside of a shutdown. But it can be normal during shutdown. So uhh... yeah: if it continues to be a problem then it needs to be reported and fixed by your distribution. What distribution are you using?

I see kernel panics at shutdown most often on Arch-based distros after updating system packages.

It sucks when it happens during shutdown but it's typically not going to cause other problems... except perhaps not automatically booting if you wanted to reboot instead of shutdown.

I'm using the XFCE edition of Linux Mint. The Kernel updated yesterday morning, could that have something to do with it?
- A kernel update, if it's done right, shouldn't cause a panic. But not every distro does updates right.
  
  If you know the old version and the new version then it might be useful to reach out to the Mint community and see if they're aware of issues like that.
  
  https://linuxmint.com/getinvolved.php -> forums or chat might be fruitful to you
on Arch-based distros after updating system packages

So basically every shutdown lol
This dude kernel panics
I see kernel panics at shutdown most often on Arch-based distros after updating system packages.

When I tried Arch, upgrading kernel would delete the kernel modules of the running kernel --- somewhat unimpressive upgrade process.
- Permanently Deleted

I'd reinstall libpcre, looks like it's gotten broken?

The kernel panic should be a direct result of shutdown (which I guess at this point is init/pid1) not finding its dependency and killing itself.

How would I reinstall it? I tried to look it up but I couldn't find anything.
- apt install --reinstall PKG_NAME
  
  Is the command to reinstall a package, replace PKG_NAME with the name of the package you want to reinstall.
  
  You should use apt instead of apt-get. It is newer, more user friendly and supposedly handles dependency resolution better.
- sudo apt-get install --reinstall
  
  https://duckduckgo.com/?q=apt+reinstall+package&t=fpas&ia=qa&iax=qa
  
  Not sure how you searched but I assume you didn't use or know apt? How do you install packages in the first place? Through GUI or Terminal?
  
  EDIT: I assume you use the Linux Mint GUI package manager. I can't find how to do this too, would need to search more detailed but I don't have enough time for this now, need sleep, don't have enough sleep.

Yes this is a kernel panic which occurs when something goes terribly wrong inside the system. This could be anything from broken software to defective hardware. You should observe if this happens regurlarly.

Ok but is there anything notable from this error message, like anything specific that I should be checking out for?
- First line of your picture is a hint for a software issue. I would just google that.

You could look at the package that's mentioned in the first line in Synaptic. The error message says it can't find a file. Fürst thing is do is check if that fike is actually there.

I might be totally wrong, but libpcre sounds like the regex library used by perl. Maybe his perl packages are broken?
- Almost. It's a C library that mimics Perl's regular expression facilities. Fairly common dependency for any number of packages.
Apt says it's installed. Someone said something about reinstalling it but I couldn't find anything online about reinstalling.

weird that it tried to load libpcre on shutdown too. have you got a wifi sniffer installed? nmap? metasploit?

I have no idea what those are, unless Linux Mint (at least the XFCE edition) has one of those installed by default, I'm pretty sure I don't have any of those installed.
Why is that weird? My shutdown is also linked against libpcre2.

Your libpcre seems broken. Reinstall the package that contains this file.

I did that yesterday and it might have fixed it because I didn't have the issue but I did try multiple things yesterday, so I'm not sure.

Personally I'd be worried there's a transient disk issue. I'd ensure my backups are good and files aren't being silently corrupted. I assume you're on an NVME, they tend to fail instantly, but sometimes you'll get transient file errors beforehand (like not being able to open a system library). Look at something like debsums to start with maybe.

I'm not having the issue anymore, I'm not sure what fixed it though as I tried multiple things yesterday.

Also, I'm not using an NVME, I'm actually just using an old laptop hard drive with one of those hard drive cases that basically converts it into an external hard drive.
- That type of error is usually indicative of hdd issue. I only mentioned NVMEs because they tend to fail all at once, without recovery options. Spining disks usually fail slower (but not always). Take a peek at smart info, maybe run a scan. My guess is the cord got jostled though tbh

As others said, check if it is a single case or if it repeats at the next shutdowns. Anyway, the main question this brings to mind is: do you have a good backup of your system / data ?

I don't have a backup of the system because if something happens, I'm switching distros. But I do have both an external hard drive and Pcloud for cloud storage for some other things like game save files.

Could also be an SEU

That's pretty specific, but I guess it's possible.
- Iirc it's 1 bit per 500mb per week for your every day ram.
  
  There's this famous case where a speedrunner playing Mario had such a bit flip and affected his play time.
Colloquially referred to as “cosmic rays”.

In addition to the other things mentioned, check the health of your drive. This could be a symptom of corruption.

You seem to have removed libpcre2 library. Try to reinstall it using your package manager.

Synaptic Package Manager states that there are several versions of libpcre2 installed, which one should I try to reinstall?

Yes, tell it you understand, and that it can happen to anyone.