DOC: Set __module__ attributes and remove core from documentation

[rhshadrach]

• closes ENH: set __module__ on top-level public objects #55178 (Replace xxxx with the GitHub issue number)
• Tests added and passed if fixing a bug or adding a new feature
• All code checks passed.
• Added type annotations to new arguments/methods/functions.
• Added an entry in the latest doc/source/whatsnew/vX.X.X.rst file if fixing a bug or adding a new feature.

This PR addresses all __module__ attributes of public objects that I can find with the exception of functions. It's not clear to me if we want to also be modifying the __module__ attribute of e.g. pandas.factorize and even if we do, I'd like to keep that separate as this PR is already becoming sizable.

Remaining documentation that contains .core.:

API docs

# Ignore redirects
grep -nre "\.core\." doc/build/html/reference/ | grep -v "has been moved" | grep -v "http-equiv=\"refresh\""

doc/build/html/reference/api/pandas.IndexSlice.html:762:<span class="sig-prename descclassname"><span class="pre">pandas.</span></span><span class="sig-name descname"><span class="pre">IndexSlice</span></span><em class="property"><span class="w"> </span><span class="p"><span class="pre">=</span></span><span class="w"> </span><span class="pre">&lt;pandas.core.indexing._IndexSlice</span> <span class="pre">object&gt;</span></em><a class="headerlink" href="#pandas.IndexSlice" title="Link to this definition">#</a></dt>
doc/build/html/reference/api/pandas.DataFrame.query.html:843:in combination with the source code in <code class="xref py py-mod docutils literal notranslate"><span class="pre">pandas.core.computation.parsing</span></code>.</p>

User Guide

grep -nre "\.core\." doc/build/html/user_guide/

doc/build/html/user_guide/io.html:3895:<span class="go">&lt;IPython.core.display.HTML object&gt;</span>
doc/build/html/user_guide/io.html:3922:<span class="go">&lt;IPython.core.display.HTML object&gt;</span>
doc/build/html/user_guide/io.html:3953:<span class="go">&lt;IPython.core.display.HTML object&gt;</span>
doc/build/html/user_guide/io.html:3984:<span class="go">&lt;IPython.core.display.HTML object&gt;</span>
doc/build/html/user_guide/io.html:4050:<span class="go">&lt;IPython.core.display.HTML object&gt;</span>
doc/build/html/user_guide/io.html:4091:<span class="go">&lt;IPython.core.display.HTML object&gt;</span>
doc/build/html/user_guide/io.html:4126:<span class="go">&lt;IPython.core.display.HTML object&gt;</span>

Getting Started

grep -nre "\.core\." doc/build/html/getting_started/

no output.

[jbrockmendel]

LGTM

[jbrockmendel]

thanks @rhshadrach

[jorisvandenbossche]

It's not clear to me if we want to also be modifying the __module__ attribute of e.g. pandas.factorize and even if we do, I'd like to keep that separate as this PR is already becoming sizable.

We already did it for the majority of functions in the top-level namespace in practice, so opened #62758 to finish that (at least for the top-level namespace)

[jorisvandenbossche]

And @rhshadrach thanks a lot for this PR!!