followed with ‘I wasn’t aware is so important to you. I didn’t want to insult you and if you felt so, I apologize. The word fuck is one I use very often, but I’ll try to control myself around you’
Note I didn’t insult the coworker (no fuck you or fuck off), but simply said ‘fuck’ out loud due to a job error.
I work in a very large tech company. I curse like a fucking sailor around some people and use my church voice around others. Expletives lose their punch when used too often.
I wouldn’t apologize or bring it up further. The time for an apology about language spoken in the heat of the moment is as soon after as possible.
The best apology is a change in behavior.
Good luck navigating this, you can see how contentious a topic it is by the comments in this thread. But it boils down to know your audience, and believe people when they tell you they have a problem.
I remember working in the London UK office and we curse non-stop over there it’s great. Whenever our colleagues from SF would visit they would always be surprised how much we swear. I’d see them do the turnaround like, ‘what just happened?’.