How have you dealt with questions by current existing colleagues when going for job interviews?

I suppose this depends on the culture at your workplace, is it more sensitive towards such topics? Also how close you are with these colleagues?
I recently gone through something similar and to most of the colleagues, I told them that I had my own appointments. But to the closer ones, I did share that I was going for a job interview.

Only for really close work buddies whom you trust. The only time I did personally was when the whole team was interviewing for other jobs, because of the toxic culture in the company.

Otherwise, I have seen cases where some nosey gossip mongers spread the word, and if it reaches HR, HR tells your manager, Manager comes to you to ask you what's going on (especially if it's a difficult manager), then GG.