Should I apologize at the scene?

The instinct to apologize is human and it's often reflexive rather than an admission of anything. The problem is how it gets used.

The distinction that matters. Checking on someone, offering help, and being courteous are appropriate and cost you nothing. Statements characterizing what happened — that you didn't see them, that you were distracted, that you were going too fast — are different, and they get repeated to adjusters and quoted in reports.

People apologize when they aren't at fault. It's a social reflex under stress. But an insurer reading "he said he was sorry and admitted he didn't see me" won't treat it as a reflex.

Nobody at the scene knows what happened yet. Fault frequently turns on facts neither driver can see — a light sequence, a sight obstruction, the other driver's speed, a mechanical failure.

What to say instead: ask if they're okay, exchange information, and let the investigation establish the rest.