How to properly link to PyQt5 documentation using intersphinx?

EDIT: I create python package with this solution: https://pypi.org/project/sphinx-qt-documentation/

ORIGINAL ANSWER:

I use another approach to this problem. I create custom sphinx plugin to translate on fly inventory file to use sip domain. It allows to chose which documentation should be pointed (pleas see docstring on top). It works on my project, but I'm not sure if it support all cases.

This extension need sphinx.ext.intersphinx extension to be configured in sphinx extension and PyQt configure in mapping

intersphinx_mapping = {...,
                       "PyQt": ("https://www.riverbankcomputing.com/static/Docs/PyQt5", None)}

"""
This module contains sphinx extension supporting for build PartSeg documentation.

this extensio provides one configuration option:

`qt_documentation` with possibe values:

 * PyQt - linking to PyQt documentation on https://www.riverbankcomputing.com/static/Docs/PyQt5/api/ (incomplete)
 * Qt - linking to Qt documentation on "https://doc.qt.io/qt-5/" (default)
 * PySide - linking to PySide documentation on  "https://doc.qt.io/qtforpython/PySide2/"
"""
import re
from sphinx.application import Sphinx
from sphinx.environment import BuildEnvironment
from docutils.nodes import Element, TextElement
from docutils import nodes
from typing import List, Optional, Dict, Any
from sphinx.locale import _

from sphinx.ext.intersphinx import InventoryAdapter

try:
    from qtpy import QT_VERSION
except ImportError:
    QT_VERSION = None

# TODO add response to
#  https://stackoverflow.com/questions/47102004/how-to-properly-link-to-pyqt5-documentation-using-intersphinx

signal_slot_uri = {
    "Qt": "https://doc.qt.io/qt-5/signalsandslots.html",
    "PySide": "https://doc.qt.io/qtforpython/overviews/signalsandslots.html",
    "PyQt": "https://www.riverbankcomputing.com/static/Docs/PyQt5/signals_slots.html"
}

signal_name = {
    "Qt": "Signal",
    "PySide": "Signal",
    "PyQt": "pyqtSignal"
}

slot_name = {
    "Qt": "Slot",
    "PySide": "Slot",
    "PyQt": "pyqtSlot"
}

signal_pattern = re.compile(r'((\w+\d?\.QtCore\.)|(QtCore\.)|(\.)())?(pyqt)?Signal')
slot_pattern = re.compile(r'((\w+\d?\.QtCore\.)|(QtCore\.)|(\.)())?(pyqt)?Slot')

def missing_reference(app: Sphinx, env: BuildEnvironment, node: Element, contnode: TextElement
                      ) -> Optional[nodes.reference]:
    """Linking to Qt documentation."""
    target: str = node['reftarget']
    inventories = InventoryAdapter(env)
    objtypes = None  # type: Optional[List[str]]
    if node['reftype'] == 'any':
        # we search anything!
        objtypes = ['%s:%s' % (domain.name, objtype)
                    for domain in env.domains.values()
                    for objtype in domain.object_types]
        domain = None
    else:
        domain = node.get('refdomain')
        if not domain:
            # only objects in domains are in the inventory
            return None
        objtypes = env.get_domain(domain).objtypes_for_role(node['reftype'])
        if not objtypes:
            return None
        objtypes = ['%s:%s' % (domain, objtype) for objtype in objtypes]
    if target.startswith("PySide2"):
        head, tail = target.split(".", 1)
        target = "PyQt5." + tail
    obj_type_name = "sip:{}".format(node.get("reftype"))
    if obj_type_name not in inventories.named_inventory["PyQt"]:
        return None
    target_list = [target, "PyQt5." + target]
    target_list += [name + "." + target for name in inventories.named_inventory["PyQt"]["sip:module"].keys()]
    if signal_pattern.match(target):
        uri = signal_slot_uri[app.config.qt_documentation]
        dispname = signal_name[app.config.qt_documentation]
        version = QT_VERSION
    elif slot_pattern.match(target):
        uri = signal_slot_uri[app.config.qt_documentation]
        dispname = slot_name[app.config.qt_documentation]
        version = QT_VERSION
    else:
        for target_name in target_list:
            if target_name in inventories.main_inventory[obj_type_name]:
                proj, version, uri, dispname = inventories.named_inventory["PyQt"][obj_type_name][target_name]
                print(node)  # print nodes with unresolved references
                break
        else:
            return None
        if app.config.qt_documentation == "Qt":
            html_name = uri.split("/")[-1]
            uri = "https://doc.qt.io/qt-5/" + html_name
        elif app.config.qt_documentation == "PySide":
            html_name = "/".join(target.split(".")[1:]) + ".html"
            uri = "https://doc.qt.io/qtforpython/PySide2/" + html_name

    # remove this line if you would like straight to pyqt documentation
    if version:
        reftitle = _('(in %s v%s)') % (app.config.qt_documentation, version)
    else:
        reftitle = _('(in %s)') % (app.config.qt_documentation,)
    newnode = nodes.reference('', '', internal=False, refuri=uri, reftitle=reftitle)
    if node.get('refexplicit'):
        # use whatever title was given
        newnode.append(contnode)
    else:
        # else use the given display name (used for :ref:)
        newnode.append(contnode.__class__(dispname, dispname))
    return newnode


def setup(app: Sphinx) -> Dict[str, Any]:
    app.connect('missing-reference', missing_reference)
    app.add_config_value('qt_documentation', "Qt", True)
    return {
        'version': "0.9",
        'env_version': 1,
        'parallel_read_safe': True
    }