How do therapists deal with their own triggers in sessions?

I saw something once saying that a therapist had a client that said something that really triggered a therapist or was a huge trigger for them and they had to manage it but I imagine that’s pretty hard to do especially in front of somebody. I wonder if I’ve ever triggered one because thus far they seem to not show it? Or like what does one say to oneself?

Sometimes there have been large silences where I’m like okay did I say something weird/bad? (I tend to be a huge over-thinker)

I have had therapists that have their OWN therapists so I wonder if it’s just they deal with it there but I’ve been curious about this because I realized of course therapists are human too of course they have their own stories and would be triggered.

I have a sort of an issue with trying to not offend people so it’s made me reluctant to open up about some stuff because I don’t want to make them feel uncomfortable even if the session is tailored towards me…