The 2N3904 is a very "generic" NPN.
The D882 is more of a "Power NPN", it will probably just work in your circuit but since it works at quite low currents in that circuit, the other transistors might be better suited.
The 2SC3650 and BCP56T1 are more similar to the 2N3904 and should both work.
To quickly classify such NPNs I look at:
Vce,max, Ic,max and \$h_{fe}\$.
2N3904: Vce,max = 40 V; Ic,max = 200 mA; \$h_{fe}\$ = 30 to 300
D882: Vce,max = 30 V; Ic,max = 3 A; \$h_{fe}\$ = 30 to 300
2SC3650: Vce,max = 25 V; Ic,max = 1.2 A; \$h_{fe}\$ > 600
BCP56T1: Vce,max = 80 V; Ic,max = 1 A; \$h_{fe}\$ = 25 to 250
If you realize how the circuit works:
When the input voltage exceeds ~12.6 V then the \$V_{BE}\$ of the NPN will exceed ~0.6 V so the NPN starts to conduct. That will pull the voltage on the collector down and enable the LM2596.
This "start to conduct when \$V_{BE}\$ exceeds ~0.6 V" is something all NPNs do (Darlington transistors also but at a higher voltage) so basically any NPN will work.