In my experience, (and bear in mind that it depends on the company and how they do their staffing), the Assistant Director was the primary person responsible for taking blocking notation for show archival purposes. As an SM, I noted entrances and exits, but I took as much blocking notation for myself as possible. As an ASM, I noted everything, esp. entrances and exits. As previously mentioned, it's helpful to have in the case of supers, but ASMs in opera are often responsible for being light walkers onstage, while the lighting designer is cueing. Having the blocking recorded will make you better prepared to walk any role you are asked to walk.
Having the entrances and exits noted is helpful for creating paperwork, like the WWW and quick-change sheets, and noting entrance cues in your score. Having all of the other blocking will help you run props in rehearsal, run any other rehearsals (like a put-in rehearsal), lightwalk, preset props, etc.
If you're an ASM, I recommend talking to your SM about it- they may have thoughts or preferences about it. Best of luck with your first opera!