Should it not have a lower case name in this case?

Yes - due to PEP8 naming convention
No - it i aiming a Site class but the right class is filled during instantiation. There is some magic to get the site class from config.py
No - it exists for 15 years https://static-codereview.wikimedia.org/pywikipedia/5088.html
No - the previous function was getSite() which was used with compat 5 years earlier
No - it would confict with site module which unfortunately conficts with Python's site namespace in Sphinx
No - it is well documented: https://doc.wikimedia.org/pywikibot/stable/api_ref/pywikibot.html#pywikibot.Site
No - it is used 101 times in framework code https://codesearch.wmcloud.org/pywikibot/?q=Site%5C(&i=nope&files=&excludeFiles=&repos=
No - it is not uncommon to have CamelCase for factory functions e.g. Django Coding style says "Use InitialCaps for class names (or for factory functions that return classes)"
No - I like that previous rule ;-)

Sorry, yes is in minority :-D

Best
xqt