Here's a small patch to do this. Everything seems to work fine.
I don't know if where I placed the test (in OtherTests) is the most appropriate.

On Tue, May 5, 2020 at 4:12 AM Domenico Ragusa <report@bugs.python.org> wrote:
>
>
> New submission from Domenico Ragusa <domenicoragusa@gmail.com>:
>
> ZipFile seems to support Pathlike objects pretty well, except in ZipFile.writestr.
> For example:
>
> >>> a = ZipFile(Path('test.zip'), 'w') # this works ok
> >>> a.write(Path('./foo.jpeg'), arcname=PurePath('/some/thing.jpeg')) # this works as well
> >>> a.writestr(PurePath('/test.txt'), 'idk') # this doesn't
> Traceback (most recent call last):
>   File "<stdin>", line 1, in <module>
>   File "/usr/lib/python3.8/zipfile.py", line 1788, in writestr
>     zinfo = ZipInfo(filename=zinfo_or_arcname,
>   File "/usr/lib/python3.8/zipfile.py", line 349, in __init__
>     null_byte = filename.find(chr(0))
> AttributeError: 'PurePosixPath' object has no attribute 'find'
>
> I think it would be more consistent if it accepted any kind of paths, it would suffice to call os.fspath in ZipInfo.__init__ when the filename is a Pathlike-object, it's just 2 lines (+ tests, of course).
>
> Can I go ahead and prepare a patch for this?
>
> ----------
> components: Library (Lib)
> messages: 368098
> nosy: d.ragusa
> priority: normal
> severity: normal
> status: open
> title: add support for os.Pathlike filenames in zipfile.ZipFile.writestr
> type: enhancement
> versions: Python 3.9
>
> _______________________________________
> Python tracker <report@bugs.python.org>
> <https://bugs.python.org/issue40506>
> _______________________________________