The first thing I must share (which is obvious , and I’m sorry ) you will need to learn basic Linux admin skills as fast as you possibly can . We can help with Plex on Linux and even teach some of the more advanced things but not equipped or staffed to teach linux itse.f
As for learning: a small VM is great for “educational sandbox” for you to safely play in without hurting anything else is perfect. You can try things, break them, snapshot restore the VM, and try again 
I don’t know which guide you might have used (there are many self-proclaimed experts out there) but it’s not difficult to do.
We have the How-To documented on our support site
You’ll find a lot of stuff here.
Additionally, I have curated a small collection of tailed How-To’s for common problems.
Back to your problem.
What you’re showing me here:
/dev/mapper/ubuntu--vg-ubuntu--lv 256862724 22079996 224066028 9% /
- ubuntu–vg-ubuntu-lv is the volume where the root file system exists
- it is only using 9% of the 256GB allocated.
That sound right?
As part of your Plex settings, in Settings - Server - Transcoder - Show Advanced
did you type in a location for the transcoder temp directory?
If you didn’t, then it’s going to use space in the root (/) partition – which is plenty.
If you configured a value of /dev/shm (shared memory for tempory space) then I can see where you’ll run out quick.
It looks like you allocated 24 GB of RAM?
If true, 12 GB can be used for the /dev/shm ‘ramdisk’.
Am I getting closer ?
Lastly, would you please type:
dpkg -l | grep plexmedia
It will tell us what you have installed for PMS.
