ORing issues and some considerations are also discussed at a high level in the TPS23753A datasheet and the TPS23754A datasheet. There are a few fundamental limitations that you might run into in trying to create a seamless switch, and in general they are concerned with the bounds on the problem. One of the concerns is the physics of the required switcher current given the (potential) difference in adapter and PSE voltages (e.g. a full power load from a 24V adapter requires 2x the current required from the PSE) and the internal sequencing/protection of the internal hotswap that can come into play during the attempt to charge a bulk capacitor from 24V to 48V while also supplying load power. If the right set of constraints and assumptions are used (e.g. 1W load), there may be solutions with cleaner switchover.
Your best chance to getting a seamless switchover is provided in the TPS23754 datasheet under "Advanced ORing Techniques" (Figure 34) where a solution with a 48V adapter and PoE voltage are seamlessly (to the load) switched. The TPS23754 had a subtle hotswap control change to enable this functionality, so it most likely will not work with the TPS23753A. The TPS23754 can be configured/used in any circuit the TPS23753A can be used in.