Would informing her colleague of the completion of the photography project be considered cutting off his livelihood, and would God hold her accountable for that, especially since she did not promise him anything, and she feels remorse for involving him in her private work?

If you promised a man to accomplish a task and you are able to fulfill it, then it is preferable to fulfill the promise according to the preponderant opinion. Discomfort or fear of envy is not an excuse to withdraw from the promise, even though withdrawing does not entail sin unless harm is intended. If there was no explicit promise, then there is no harm in withdrawing from accomplishing the task, and that is not considered cutting off his livelihood.