Purpose of backup fuse in SPD
From: Installation Instructions



F2 is a parallel backup fuse.  If I ≤ 250A F1 will open.  But if I > 250A, F1 and F2 will open to protect circuitry. 

From Overvoltage Protection of Low Voltage Systems  By Peter Hasse:


  For the TN-system overcurrent and residual protective devices are permitted for 'protection in case of indirect contact'. Lightning current and surge arresters (classes B and C) may only be installed behind overcurrent protective devices for 'protection in case of indirect contact' to safeguard measures of personnel protection also in case of an arrester fault.


There is more there in the Hasse link, but F2 is there to protect the circuit from a current surge (class C) or a lightning strike (class B).  You also have over-voltage protection (class D).  Relative Reference: IEC 61008-1.