How do you include a translatable string in an update hook In D7 you had to use get_t() in order to include translatable strings in an update hook. Is there a similar procedure for D8?
No. Just call t().

get_t() was actually for early install and things like that, update functions AFAIK didn't need it (calling t() there is however often pointless, as it is highly unlikely that there is a translation for it already when you run the updates.)

t() calls a service now, and it will use the correct one depending on the situtation automatically.