Volume on RN4220 read/only - trying to understand btrfs

"Unallocated" is precisely what that space is -- not yet allocated to either data or metadata.  It would be allocated as needed as you add files if the volume had not gone read-only.  In other words, you are not out of space and should not be trying to do anything regarding that.  Even if you were out of space, you can't do anything about it with the volume read-only.

The message you are getting when trying to create a new folder is because it cannot allocate any space for it.  It's incorrectly telling you that it's because the volume is full -- it's because the volume is read-only.  As far as what you are deleting, I suspect you aren't -- if you were to reboot (which, as I said previously, you should not attempt until you are sure you have a complete backup), I think you'll find the files are still there.

I had a volume do the same thing.  In my case, I knew why.  It was in an EDA500 eSATA expansion chassis that had the connection come loose.  I Googled everything I could about making it read/write again, and nothing I did survived a reboot.  Most of the time, it went back to read-only as soon as I tried to add a file.  Ultimately, it was dead on a reboot, forcing my had to delete and re-create it.  Since the cause of your volume going read-only is obviously different (no external chassis), maybe you'll have better luck.  But I rather doubt it.

As for BTRFS being a poor choice, a lot of file systems would, at this point, likely be unavailable.  Instead, yours is read-only so you can at least make a backup.  I'm not sure why you think that's a bad thing.