Disk Utility fails with OSStatus error 22 during cloning/recovery operation
I came here because I was looking for solutions about the error you quote, but instead your actual questions at the end of your text are about something else. It would be nice if you'd change your question title accordingly.

To answer your questions about recovery partitions:


If you install, even temporarily, a newer macOS, you should get a newer recovery partition along with it. I, for instance, have a separate 10.14.6 recovery system on one of my Macs (however, I wonder how that came to be, as there's also a Recovery APFS volume insider the container where the Mojave system resides, so why would there also be a HFS+ partition with one?). Be aware that if you install a newer system on your current system disk, it might convert your current system volume from HFS to APFS. To prevent that, install it to a separate partition (though even then I'm not sure that Apple won't simply convert all volumes on the disk to APFS), or best install it to an external disk.
Converting it into APFS is not needed and inadvisible - it would not gain you anything. Basically, the Recovery system is just a small EFI-based loader that'll then load the BaseSystem image into a RAM disk and load the Recovery system from there.
I have copied entire HFS+-formatted recovery partitions to external USB disks, so I assume you could as well copy them onto a USB stick, as long as you format it with a GUID partition scheme first. The copy operation may be tricky, though - ideally, Disk Utility should let you do that with its Restore command - but it turns that that the new Disk Utility won't even show Recovery partitions any more, so that's not an option. The old Disk Utility from pre-10.11 systems may be able to, still.


Here's what still works in my testing on Mojave with Terminal commands to copy a HFS+ formatted Recovery partition to an USB thumb drive (with GUID partition scheme):

asr --source /dev/diskVsW --target /dev/diskXsY --erase


Where diskVsW and diskXsY are the identifiers for the source and dest Recovery partitions that you'll find with diskutil list.

You could also use hdiutil to create an image file of another Mac's recovery partition and then later restore that with Disk Utility.

Also keep in mind that modern Macs can always load a recovery system from the internet, so there's no need to keep one around for them.