For example, I've switched the breaker of my workspace from B13 to C13, which both trip at above 13A (plus some) continuous, but C13 has a higher limit for short pulsed loads.
If you take a look here, you can see that a "B" breaker accepts 1 second of 5x load, while C allows for 1 second of 10x load, so up to 130A surge and more for shorter periods. https://www.klocknermoeller.com/faz/faz.characteristics.htm
They absolutely do - NTC, and they even have a relay to bypass the NTC after the PSU has booted up. If you hear a click after booting up, there is a bypass relay.
>Often when I turn on power right after a power loss, the circuit breaker immediately trips.
The circuit breakers (domestic) tend to be B or C class, B triggers much easier than C, the latter tend to be used for motors, stuff with high inrush current. If you believer you have too much inrush current, you might wish to replace the breaker. Also, the PSU datasheets specify how many of then can be connected in parallel to the same breaker.
Last but not least - if you have too much inrush current, it's likely there is no power factor correction either, so the high value caps are connected straight after the bridge rectifier.
SMPSes all have input stages that effectively directly rectify the incoming mains to provide the SMPS internal bus voltage. This is also a great way to basically design an inrush current simulator (diode(s) + big capacitor).
Adding stuff like active PFC correction in your common wall-wart is a non-starter. Those things are already massively cost-optimized.
Also note that there are different breaker classes for different loads, with the more-forgiving ones having tighter demands on the insurance of the downstream wiring, because they have to still reliably trip instantly from a short.
Often when I turn on power right after a power loss, the circuit breaker immediately trips. I assume it's because all those power supplies have such a big inrush current that they overload the circuit. All these devices use less than an amp in total on average, but the inrush current is enough to immediately trip a 13A circuit breaker.