I have the following opinion for your consideration.
"...here, the secondary L-L Voltage is 690, therefore the L-N comes around 400V; not much single phase equipment operates at 400V".
1. In this case, it is beneficial to have in Star with L-L=690V. All standard IEC LV motors with 6 terminals wound for delta 400V are suitable for 690V in Star connection. See 3 below.
2. The motor wound in delta 400V can be connected in star 690V without any change in the output Power kW rating and the direction of rotation. No rewinding is required. The current is reduced by the 400/690 = 0.579 ratio.
3. Info: For Star 690V, connect [L1-U1, L2-V1, L3-W1, link W2-U2-V2], or [L1-W2, L2-U2, L3-V2, link U1-V1-W1].
Che Kuan Yau (Singapore)