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.
That depends massively on the profession, setting, and context.
Restaurant kitchen where something gets spilled, a trade where something unexpectedly breaks, a couple lawyers without anyone else around finding out their client is on camera admitting to the crime, etc. are all fine to say a calm ‘oh fuck’ as a reaction. Someone in an open office who yelled it because their code didn’t compile would not be acting very professional.
OP is a nurse in a hospital.
If no patients were around then an excited utterance gets a free pass.
It may be more common among certain job types, but I don’t think that makes it professional behavior to do so regardless of the type of work.
Found the op’s coworker.
Any outburst would be unprofessional, a specific word changes nothing unless directed at someone.