Who is the actual formation excusal authority (if it is explicitly stated)?

So there are a few things at work here.

First, there is probably a reason the CO/1Sgt are making this call and taking that stance.

It isn't uncommon for Plt Sgts and Plt Commanders to cover for their people while they are handling issues whether it is work related, family issues, medical/dental etc. That is normal but it is also normal for the head shed to crack down when things happen and people abuse the system. So leadership discretion takes alot of space in this realm. The best thing you can do is for the Plt Sgt and Plt Commander to build a relationship with not only their troops but their next level leaders because those relationships or lack thereof will dictate how this goes.

The authority of the Company Commander is basically everything not prohibited by AR or by higher. Can the CO order notifications before excusing someone from Formation? Absolutely. That is called Command Authority. He can delegate the to whomever he pleases. Just as his boss, the BNCO, can mandate rules for formation, PT, etc as long as they are within his Commanders guidance and Regulations.

The CO is accountable, but the 1SG is responsible for accountability. Generall, for a Company formation, the PSG is reporting on the status of Soldiers - which means that PSG had better know and approve of any absences, because (s)he will be the person answering the hard questions.

Likewise, for a BN Formation, 1SG is answering for missing Soldiers, so 1SG had better know and approve of absences. And on and on.

But ALL of it starts at the Team Leader level. Soldier notifies TL of reason for absence, and TL starts running it up the chain. And if there is even a LITTLE bit of question, generally that PSG is going to pre-approve with 1SG (or 1SG with CSM). Most units have an informal "acceptable excuse" list. Sick Call, Appointment, duty recovery, taskings, etc. are known things that the PSG can simply report "1 on sick call, 2 on leave, three on detail" and be good to go. But if the 1SG/CO puts out "100% presence, THAT is when the PSG starts getting that pre-approval.

At the end of the day, though, essentially EVERY formation is "no one misses, unless we know about it" because the PSG SHOULD be getting accountability at every formation and reporting absences, along with excuses (even if 1SG does not order a report). This is trebly true for the first formation of the day (usually PT) which is generally considered an "accountability formation."

For all of our BN (and higher) formations, where 1SG (or CSM) was up front, I was always accounting for all my folks, and reporting to 1SG prior to that first "Fall in," even if it wasn't a "formal" report like at morning formation.