The point is that a manufacturer does not tell you how he has implemented the "temperature stabilized" Zener component. One way to find out if it was a buried or a surface Zener is looking at noise level. The ones with a very low noise level are most probably the buried ones. A lot of datasheet explicitely mention the word "Zener" and not "Bandgap". When you look at TIs datasheet showing the internals of the chip the 6.2 zener is explicetely drawn.
In the course of chip shrinking over the decades manufacturers have sought ways to replace the Zener by a bandgap or similar circuit with some tempco improving circuitry. One of them was ST, and the results were mixed. The new chips have a much higher drift factor than the old ones (I keep a box of all kinds of 723s from different manufacturers and dates). They (TI the same) had (before discontinuing the part altogether) some customer response claiming problems with drift values a lot higher than the datasheet suggests. The explanation was a "trapped charge" problem you never have with a subsurface Zener. So, they tried to cut corners.
An "official" bandgap 723 clone product was the SG3532, with about 2.5V of reference voltage, more accurate current limiting, overtemp protection and some other gimmicks. It was discontinued because the LM723 was good enough for most users and the SG3532 niche was too small.
Mil versions are a totally different story. The drift for a few days, and then stay tack sharp for a long time. The old ones were definitely aged and temp cycled, and most probably used a buried Zener.
https://electronicprojectsforfun.wordpress.com/silly-circuits/silly-circuits-a-heated-lm723-reference/has some details about the stability experiences with several 723 types, including long-term results.
I am OK with the definition of drop-out voltage as the minimum input/output voltage where the part still provides regulation. In the case of the 723, the built-in reference needs at least 9.5V (varies by datasheet) on the Vcc pin. The Vc pin can be lower, agreed. So, the manufacturers took the maximum of both voltages to be correct. When you look at my "best practices" you see exactly this ("headroom"). The minimum Vc voltage can be computed from the minimum output voltage (2V), the drop on the current limiting resistor, plus some headroom for the 723s internal pass transistor, so you end up with something in the ballpark of 4-5V, at not too high currents.
Apology accepted if you promise me that you read stuff to the end.