According to [1] there's no concensus on which minimum Sphinx version we should use for Python 3.10.

"sadly" since https://github.com/python/cpython/pull/23620 which make use of a Sphinx 3.2.0 only feature, we should bump it to 3.2, but it may not work for everybody.

[1]: https://github.com/python/cpython/pull/23620#issuecomment-755420205

In favor of Sphinx 3 only :

- We have :no-trim-doctest-flags: which fixes https://bugs.python.org/issue36675
- backslash handing is different in Sphinx 2 and Sphinx 3: https://bugs.python.org/issue42822


In favor of keeping compatibility with Sphinx 2 :

- Some distribs may want/need to ship Python 3.10 along with Sphinx 2?

So I'm personally in favor of a full witch to Sphinx 3 with Python 3.10, but I'm open to hear everybody.

> Some distribs may want/need to ship Python 3.10 along with Sphinx 2?

In my experience, Linux distributions prefer to only ship a single Sphinx version. The question is more which Linux distributions are stuck at Sphinx 2 only?

If there is a short list of Linux distributions which cannot use Sphinx 3, even just to build the Python documentation, would it be acceptable for them to stop shipping the Python documentation?

In Fedora, the Python documentation is a separated package. For example, it allows us to upgrade Python while Fedora Rawhide was upgrade to Sphinx 3 but the Python documentation was not compatible with Sphinx 3 (fixed in bpo-40204).

If you ask *me*: I mostly care about Fedora which already uses Sphinx 3.2, so I'm fine with requiring Sphinx 3.2 (the Python documentation is *not* compatible with Sphinx 3.0 and 3.1: see bpo-40204).

If the minimum required Sphinx version changes, please document it properly at:
https://docs.python.org/dev/whatsnew/3.10.html#build-changes

Ah, the issue is also being discussed in PR 24142 comments.

* Fedora 33 (stable) ships python3-sphinx 3.2.1-1 and python3.10 version 3.10.0~a3-1 (the alpha4 is under tests).
* Debian Buster (stable) ships python3-sphinx 1.8.4-1 and python3 version 3.7.3-1
* Debian Sid (unstable) ships python3-sphinx 3.4.3-1 and python3 version 3.9.1-1.
* Ubuntu Groovy (stable) ships python3-sphinx 3.2.1-1 and python3 version 3.8.6-0ubuntu1
* Ubuntu Hirsute (dev) ships python3-sphinx 3.3.1-1 and python3 version 3.9.0-3ubuntu1

In this list, requiring Sphinx 3.2+ to build Python 3.10 documentation would only be an issue on Debian Buster.

I didn't check Red Hat RHEL or SUSE SLE. If they want to ship Python 3.10 but only have an old Sphinx, they can either use a newer Sphinx to build the doc, or ship Python 3.10 with no doc (since it would not be the "system Python", it may be an acceptable tradeoff).

There is a PPA on Ubuntu for Python 3.10. The PPA maintainer considers the drop the documentation, see discussion at:
https://github.com/python/cpython/pull/23620#issuecomment-755423140

Ubuntu 20.04 LTS still sees subminor Python 3.8 version updates, and needs to use sphinx 1.8.5.

New changeset 5c1f15b4b1024cbf0acc85832f0c623d1a4605fd by Julien Palard in branch 'master':
bpo-42843: Keep Sphinx 1.8 and Sphinx 2 compatibility (GH-24282)
https://github.com/python/cpython/commit/5c1f15b4b1024cbf0acc85832f0c623d1a4605fd