"Sorry for asking is just manners"
Some readers will defend the softener as a matter of form. You're asking someone to do something for you. Manners require an acknowledgement. Sorry is the acknowledgement.
Peter Kim and colleagues, in 2004, studied when apologies repair trust and when they don't. They distinguished two kinds of violation. Competence violations, where someone got something wrong, and integrity violations, where someone was dishonest or acted in bad faith. Apologising worked for competence violations. For integrity violations, when the person was innocent, denying it worked better than apologising, because an apology for something you didn't do reads as an admission. The study is about workplaces and alleged wrongdoing, and I'm using it for one narrow point. An apology is understood by the listener as an admission of something. It implies a violation, and the listener looks for one.
Asking a colleague a question isn't a violation of anything. It isn't a competence lapse and it isn't a matter of integrity. It's the ordinary traffic of a workplace. When you open it with sorry, you've told the listener there's a violation somewhere in what follows, and they look for it, and the only candidate is the question itself. So the question gets filed as the violation. The colleague, who'd have answered "when's the deadline?" without a thought, now answers a person who's confessed to intruding, and part of them agrees.
Manners do require an acknowledgement, and there's a word for it that isn't an admission. It's thank you. "Thanks, that's really helpful" acknowledges the colleague's time after the fact, when there's something to acknowledge, and it costs no competence at all, because thanking, in Chaudhry and Loewenstein's account, is the one of the four that gives credit to the other person without taking blame onto you. That's the thanks swap, and chapter 21 is about it. Sorry before, thanks after, become thanks after and nothing before, and the manners are intact.
"Sorry for asking" isn't manners. It's a confession to a crime that hasn't been committed, offered to a person who wasn't going to charge you, and the confession is what puts the idea in their head.