Trailing white space stripped from doctests

Describe the bug

This doctest fails, and I don't think it should:

>>> text = '''foo
... bar 
...  baz
... ba t
... '''
>>> print(repr(text))
'foo\nbar \n baz\nba t\n'
>>> text.count(' ')
3

The reason it fails, is there is a trailing space after "bar" (on line 2), but this is eliminated before the source is passed to doctest, thus text is assigned the value foo\nbar\n baz\nba t\n instead of foo\nbar \n baz\nba t\n. Whilst I generally really hate trailing white space, if the space matters... then it matters... So report is:

**********************************************************************
File "index.rst", line 9, in default
Failed example:
    print(repr(text))
Expected:
    'foo\nbar \n baz\nba t\n'
Got:
    'foo\nbar\n baz\nba t\n'
**********************************************************************
File "index.rst", line 11, in default
Failed example:
    text.count(' ')
Expected:
    3
Got:
    2
**********************************************************************

Invoking doctest on the rst directly the test above passes no problem.

How to Reproduce

$ mkdir foobar
$ cd foobar
$ python3 -m venv venv
$ . venv/bin/activate
$ pip install sphinx
$ sphinx-quickstart --sep --project foobar --author 'Does Not Matter' --release 0.0.1 --language en --ext-doctest
$ cat > source/index.rst 
foobar
======

.. doctest::

   >>> text = '''foo
   ... bar 
   ...  baz
   ... ba t
   ... '''
   >>> print(repr(text))
   'foo\nbar \n baz\nba t\n'
   >>> text.count(' ')
   3
^D
$ make doctest

Expected behavior

Doc test illustrated above passes.

Your project

N/A

Screenshots

No response

OS

Linux

Python version

3.8.10

Sphinx version

4.3.0

Sphinx extensions

No response

Extra tools

No response

Additional context

I had a little look into it and I can see the source is serialised with pickle in build/doctrees (in this above case), with the space missing. Or at least getting it back out the space is missing by that point anyway.

Reproduce the failure with the provided Sphinx project and make doctest, then inspect the doctest source as it is serialized in build/doctrees. Trace where the trailing space disappears before execution; done means the example preserves it and passes with the expected count and representation.