how does l6565 IC VFF function function
These are two different ICs. The 1st one is a classical quasi-square-wave resonant controller also called QR controller while the second is a true PFC controller. What they call voltage feed-forward is a means to limit the maximum power between low- and high-line operations. In a QR converter, at low line, the switching frequency is low and the peak current setpoint is close to its maximum at nominal power. Should you increase \$P_{out}\$ slightly and the over current protection kicks in. At high line, the switching frequency will naturally be higher, requiring a small peak current setpoint to pass the same \$P_{out}\$. Therefore, the distance between the peak current at high line and the maximum limit is larger than at low line. There is a lot more power you can deliver before the protection trips (often x2 or more).

What ST probably does with this pin is they offset the current sense pin information with a level proportional to \$V_{in}\$. They can also reduce the max setpoint in relationship with \$V_{in}\$, it is the same. At low line this offset is small and the maximum peak current limit does not change but at high line, this offset is larger and you "touch" the limit sooner. See the below picture showing how this over power protection or OPP was performed with the former UC384x controllers:



The principle is the same. Assume the max current sense voltage is 1 V across a 1-ohm resistance. With a 0-V offset, the maximum current you accept is 1 A. Now assume that you bias the CS pin with a 200-mV dc offset. Then the voltage dynamics is no longer 1 V but 800 mV. The maximum authorized current is therefore 800 mA. If this offset is linked to \$V_{in}\$ as shown in the picture, then you limit the maximum output power in high-line conditions. If you want to know more, check this link and this one. Both fixed-switching frequency and QR types are covered.