What are the purpose of C38 to C51 in this design?
The short answer is lower supply ripple.from switched load regulation noise which is caused by DC Ω's = DCR of the motor

If you look closely at the switched load and RdsOn of the switches and ESR of the Caps, you should expect the ESR of the the string of Caps to be much less so than the load DCR. ... Perhaps near the RdsOn of the full bridge.

If you look at any family of caps you should expect as parts get bigger in value the ESR gets smaller but also the self resonant frequency gets smaller. In fact for the same voltage and size the ESR * C is fairly  constant  in any one design family of caps.

Also each cap has a small ESL [nH] which can affect ringing in the commutation and controls the self resonant freq (SRF) and having a parallel bank of caps also reduces ESL by N caps 

Note the large top side copper plane on each side of the caps.  These are also important design aspects to reduce power source inductance which can affect load regulated supply noise.

With low profile ultra low ESR caps as I expect these are I would expect the low ESR*C time constant to be in the 1-10 µs range and std caps in the 100 `300µs range.  THis changes with cap design of materials, size and voltage over a wider range. This is just a rule of thumb that is 100x better than 40 years ago.

Thus for a good design of caps,  T=ESR*C = 1 µs and C= 10uF each cap could have an ESR hypothetically of 100 mΩ and thus 14 parallel caps will be ~ 7 mΩ.

Not looking into the actual load impedance of this design, if you examine the specs for these cap and motor switches and motor ESR, you should find the caps make an adequate voltage source so step pulse ripple is &lt; 5% for example.  From this spec you can work out the ESR : Rds + DCR of motor ratios to minimize heat losses in the switches and caps for a reliable design.