The idea with motors, is that to successfully start, they draw a lot of current until they are in sync with the supply frequency. A motor which, due to volt drop, is unable to get to speed quickly, will overheat due to the high current it is consuming, and could suffer damage. Various methods are used, to limit the initial current draw, such as reducing the mechanical load until up to speed, resistances in series to limit the draw, and with 3ph star- delta starters.
Some systems include low-voltage releases, to protect motors from voltage dropping at start up.
All of this is spot on and yes we do need to consider all of it.
However unless the generator volts are below expected and/or the pump rating is close to the generator capacity (I imagine neither of those apply) I'd expect volt drop to be acceptable and to be honest a 1.5mm² will probably work perfectly although I'll say don't be tempted to give it a try, it will be a bad false economy and very likely bite in the future.
To explain this and as I say don't try it. Working on this calculation:
We see a 25V drop at 2.2KW (capacity of generator)
The following ramblings ARE NOT THE WAY TO DESIGN A CIRCUIT but hopefully offer an insight to real world expectations.
Our existing mains supply is stated as 230V +10%/-6% (253-216.2) so in theory; if running at that full load current, the 25.2 voltage drop can be added to the spec which allows the generator to run at 278.2 - 241.4V to give our required supply.
In practice your pump is unlikely to be drawing 2.2KW. My limited experience of bore hole pumps is 0.75 and 1.2KW and those smaller loads will result in overvoltage if the generator is not limited .
IF the generator is running (in spec) between 253 & 241.4V (quite typical for older units) then the final voltage will be within spec for a load at 2.2KW or below.
From the above screenshot it can be shown that purely on voltage drop a smaller cable will often APPEAR to be acceptable but there are other factors to be considered. For example that length of 1,5mm² cable from the above calculation (I have not double checked this against Ω/m chart) gives 2.7Ω and a short circuit on a supply the minimum of 216V is 80A which is right on the 5X figure for magnetic tripping a B16 MCB, allowing for any other resistance in the system especially with connectors permanently in damp situations it doesn't take too much for a short circuit to take a minute or ten to trip a breaker especially if someone has fitted a type C or D 'because it's a motor'.
As I mentioned this rambling is not the way to design circuits.
Personally I'd consider 4mm² minimum but I haven't got all of the details (pump rating) or done all of the calculations.