UPDATE - a beta release of THG 6.1.2 apparently has restored hggit and is available now:
https://foss.heptapod.net/mercurial/tortoisehg/thg/-/issues/5752#note_185806
I haven't tried it yet myself.
That post also notes:
The plan is for a py3 installer to be available with the next major
release [in July 2022]
Original answer:
Apparently at the moment THG has the option to include hggit in the settings, but does not actually package hggit itself.
According to Matt Harbison, one of the contributors/maintainers of TortoiseHG:
I took [hggit] out because it was always lagging behind changes in core hg,
and its dependencies broke stuff.
He goes on to add:
install by simply running py -2 -m pip install hg-git --user
if you
have python2 installed on your system.
Another person (Aurélien Campéas) states the following for using Python 3:
with python 3 and a plain "pip install mercurial hg-git" and it just
works
Further, this other post by Keith Turkowski describes a full installation of THG and hggit with Python3 on Windows:
Install python-3.9.2-amd64.exe (if you want to use Python 3 and have Python.exe in the path)
Install putty-0.74-installer.msi (for SSH support)
Install tortoisehg-5.7.0-x64.msi
Install python-2.7.18.amd64.msi (For current user, Python.exe not in path)
Win+R -> cmd
(command prompt): py -2 -m pip install hg-git --user
Enable hggit in TortoiseHg Settings (Extensions)
I assume you could use newer versions of the THG, Python, etc. installers.