How can I manually update the URI of an entry? Is there a way to manually change the URI for an entry?
for instance where is this stored in the database (is it?)

I need to update one that is: /vacancies  to /vacancies-1444 for example
the 1444 never got added to the URI when created by an API entry creation and /vacancies is the root of a list of vacancies.
For most cases, it should be as simple as updating the slug for that entry to vacancies-1444 on the entry edit page.

This is assuming it's not in a Structured Section and you haven't defined some custom URI rules where the last segment of the URI isn't {slug}.