Python 3.7 is affected as well:

vstinner@apu$ ./python -Werror -m test test_docxmlrpc
----------------------------------------
Exception happened during processing of request from ('127.0.0.1', 46636)
Traceback (most recent call last):
  (...)
  File "/home/vstinner/prog/python/3.7/Lib/xmlrpc/server.py", line 828, in docserver
    contents.append(self.docroutine(value, key, funcs=fdict))
  File "/home/vstinner/prog/python/3.7/Lib/xmlrpc/server.py", line 791, in docroutine
    formatvalue=self.formatvalue)
  File "/home/vstinner/prog/python/3.7/Lib/inspect.py", line 1225, in formatargspec
    stacklevel=2)
DeprecationWarning: `formatargspec` is deprecated since Python 3.5. Use `signature` and the `Signature` object directly
----------------------------------------
Warning -- threading._dangling was modified by test_docxmlrpc
  Before: <_weakrefset.WeakSet object at 0x7fc84da8f810>
  After:  <_weakrefset.WeakSet object at 0x7fc84da8f538> 
test test_docxmlrpc failed -- multiple errors occurred; run in verbose mode for details
test_docxmlrpc failed


I generated PR 8294 backport to fix Python 3.7 as well. Since the HTML output is unchanged, IMHO it's safe to backport the change.

In the documentation, inspect.formatargspec() is also deprecated in Python 3.6, but the code doesn't emit a DeprecationWarning. I don't think that it's worth it to backport the change to Python 3.6.