Well, to answer your original question - yes, it will be as alright as the 3kW one on the circuit.
However, it is a very poor design as the 13A which the shower uses only leaves 3A for the other eight things, presumably sockets but we don't know, on the circuit which is likely to cause tripping and wear on the MCB.
We cannot say why it has been fitted with a 16A MCB.
It may be possible to increase this but we cannot tell from here.
It does say in the instructions that it should be fitted with a Fused Connection Unit but some 13A accessories and fuses don't like 13A currents.
However, it is a very poor design as the 13A which the shower uses only leaves 3A for the other eight things, presumably sockets but we don't know, on the circuit which is likely to cause tripping and wear on the MCB.
We cannot say why it has been fitted with a 16A MCB.
It may be possible to increase this but we cannot tell from here.
It does say in the instructions that it should be fitted with a Fused Connection Unit but some 13A accessories and fuses don't like 13A currents.