Yes, I can confirm this. Dvorapa already added example which happening on my private wiki. :)

insite parameter of pywikibot.Page uses code of a specified Site. For Mediawiki (single site family) the code is the same as family: mediawiki. But interwiki is only either mediawikiwiki or mw. Therefore insite parameter should get and use interwiki prefix of the specified Site, not the actual code

Change 414070 had a related patch set uploaded (by Zoranzoki21; owner: Xqt):
[pywikibot/core@master] [bugfix] iw link for mediawiki is mediawikiwiki

https://gerrit.wikimedia.org/r/414070

if insite:
    target_code = insite.code
    target_family = insite.family.name
else:
    target_code = config.mylang
    target_family = config.family
if force_interwiki or \
   (allow_interwiki
    and (self.site.family.name != target_family
         or self.site.code != target_code)):
    if self.site.family.name != target_family \
       and self.site.family.name != self.site.code:
        title = '%s:%s:%s' % (
            self.site.family.name, self.site.code, title)
    else:
        # use this form for sites like commons, where the
        # code is the same as the family name
        title = '%s:%s' % (self.site.code, title)

The last line causes this issue.

In my opinion it should use Site.interwiki_prefix() instead of Site.code (and the lines above too in some way).

Site.interwiki_prefix() needs to be fixed before:

• T188179: site.interwiki_prefix() method always fails
• T222026: Site.interwiki_prefix() should not fail if the interwiki is indirect

The same issue is for test / testwiki

Change 509538 had a related patch set uploaded (by Dvorapa; owner: Dvorapa):
[pywikibot/core@master] [bugfix] Fix mediawikiwiki and testwiki shortcuts

https://gerrit.wikimedia.org/r/509538