[Archery][CI] Refactor git dependencies used on archery to be more consistent

[asfimport]

Currently archery has the following git related dependencies:

    'release': ['gitpython']
    'crossbow': ['github3.py', 'pygit2>=1.6.0']
    'crossbow-upload': ['github3.py']
    'bot': ['github3.py', 'pygit2>=1.6.0', 'pygithub']

that makes difficult to work with archery git related code and makes more difficult code reuse. As an example the comment on this PR: #14033 (comment)

While dev/archery/archery/crossbow/core.py uses pygit2, dev/archery/archery/release/core.py uses GitPython. The Repo class that is used in each module are also not shared. 

We should refactor archery to not require 2 different github libraries (github3 and pygithub) and 2 different git ones (pygit and gitpython).

Reporter: Raúl Cumplido / @raulcd

_{Note: This issue was originally created as ARROW-18038. Please see the migration documentation for further details.}