reasons why shadowgast would not get married:
Essek does not legally exist in the Empire, so the courts would not recognize the marriage
the Dynasty probably would recognize the marriage but Essek can't go back there cause of the whole treason and war crimes thing
while they both respect their cleric friends, neither of them particularly want or need a god weighing in on their relationship
changing last names would be way too much hassle for Caleb since he's been known professionally as Widogast for years, and pointless for Essek because he doesn't use his real name in public anyway.
they're both too introverted to want to throw a big party in honor of them being in love.
neither of them are huge fans of tradition, so getting married has no symbolic meaning for them either
idk when you've been living together for years and you have 2 cats and you're touching spellbooks and going to wizard hell aeor for dates, a marriage wouldn't add much more to that.
reasons why shadowgast WOULD get married:
squishy wizards get +2 to AC for a week