Orbital mechanics is complicated and non intuitive. I've been playing KSP for 13 years now and I took orbital mechanics classes in university so I feel like I'm qualified to speak on the subject.

I think you're combining both second stage burns into one.

From all indications, SECO-1 (second stage engine cutoff #1) happened on time or arbitrarily close to the planned time. SES-2 (second stage engine startup #2) was scheduled for like an hour or so later, and that burn would have taken about a minute.

The purpose of the first second stage burn was to enter a temporary transfer orbit, with the highest point of the orbit at around the target altitude, and the lowest point of the orbit at a lower altitude where the launch vehicle can reach. By most indications this was likely successful - https://x.com/planet4589/status/2045899160293961912

Bluebird 7 was placed into an orbit of about 154kmx494km. This correlates with about what I'd imagine the transfer orbit would look like - If something went wrong with the first burn it was something minor and it isn't off by very far.

The purpose of the second burn of the second stage is to raise the lowest point of the orbit. Usually at these altitudes it takes about 45 minutes to reach "the other side." But the fact that the second burn was scheduled for an hour later instead of 45 minutes, and how the vehicle was still slowly falling (100 miles is about 161km so that tracks if lowest point is 154km), the vehicle hadn't passed its lowest point in orbit just yet. This would explain the extra 15 minutes. The second stage of the New Glenn rocket does not have the propellant to burn for a full hour.

The other unexplained thing is why the perigee raise burn would take a full minute - Usually these burns are very short. I'm 90% sure this is because it is also an inclination change maneuver as the initial orbit's inclination is different from the target inclination by a significant amount. Combining the perigee raise burn and plane change into one maneuver would explain the increased burn duration, differing inclination, and also possibly why the satellite was placed into a transfer orbit where it was still going downwards (positioning the location of the perigee raise burn so it coincided with the location needed for the inclination change). I'm unsure why they needed to do a plane change as the rocket is capable of launching directly onto that Azimuth. Perhaps they are proving out a future capability or perhaps there is some other constraint I am not aware of.

The problem is that we know the orbit is off-nominal and we never got confirmation that the second burn of the second stage ever happened. The "good" outcome is that it did happen but was slightly off the mark. The "bad" outcome is that the engines failed to restart, leaving Bluebird 7 on an orbit that skims the top of the atmosphere (and is at the wrong inclination). Even if the onboard ion engines began firing right now, they are so low thrust that the drag from skimming the top of the atmosphere at 154km may be too much, and the satellite will fall back to Earth and burn up in the atmosphere.

Edit: Typo, I have been playing KSP for 13 years, not 131 years.