I Am British

The specific use of "sorry" which you mention is interesting. Here, of course, we use it to convey contrition for what we perceive as our own part in something which went wrong; this is the meaning of "sorry" in the phrase "Love means never having to say you're sorry."

Do you distinguish between the apologetic use of sorry--"I am sorry that I was unable to make the beginning of the meeting..."--from this interjection-esque usage...?

It is odd that the British would do this, since it

1) calls attention to something which went amiss with someone else (thus, exacerbating an already-uncomfortable situation and making the person feel worse), and

2) shows concern for others even in situations where you would only be an observer, not a participant (violating stiff upper lip for oneself and as a model for the other person).

While the latter might be too much of a stereotype, I thought that good manners were designed to prevent the former...?

(I have heard many people who learned British English as a 2nd, 3rd, etc., language say "sorry" but seemingly more when they were involved in some small problem/error/misstep.)

[Edit: removed draft artifact.]

I never comment like that if I bump into someone. I always say, "I'm so sorry, excuse me". I'm an American who was brought up with manners.

We once had those manners too....
Well, some of us still do

Keep on doing you.

Someone told me to stop saying sorry once, and I said "Sorry" even to that.

People seem to have forgotten that I'm sorry doesnt just mean "I apologize for what happened to you" but also "I regret that this happened" i.e. without assuming blame

Hmm, maybe it also depends on the person. I know some people like that

Yeh same lol. I'm always like oh no sorry I stood on your toes like

Most British are polite