Schottky diodes are just used for lower forward voltage drop. Standard rectifiers could be used with some loss of efficiency or transistors could be used for greater efficiency.
The first diode isolates the panels from the battery when operating on battery and the second diode isolates the battery from the panels when operating on the panels. This mode of operation will not be suitable if the load is expecting a restricted voltage range because the panel voltage is not regulated.
The application examples at the end of the datasheet lack both diodes and connect the load directly to the battery
I should correct by saying that Schottky diodes have no recovery because of design. No p-type semiconductor so no holes when reverse biased. So nothing to recover.
That is not strictly true in most cases. Because of how high voltage schottky diodes are constructed with a guard ring, which is practically all of them, they have an additional PN junction in parallel so at high currents the PN junction also conducts creating reverse recovery which is revealed as a long recovery tail. In most applications this can be ignored unless the peak currents are high.