Thats slightly over 5%. I agree it's not too concerning.
Normally not so much an issue unless it is creating a drop that is affecting other equipment or lighting. Neither of which was mentioned by OP. But there are several threads that ask about light flicker or other effects when washer running.
So I wonder if the drop mentioned by OP is strictly on the washer line or more global to the entire panel or service.
It is normal to see an amount of drop when a load, particularly motor loads, are switched on as load is applied. Another test is what happens to voltage during the spin cycle, is the voltage drop continuous during the load application or just during startup?
If OP is concerned, if drop is continuous during the continuous load application, one consideration might be to investigate terminations, loose terminations can, when load is applied, create a loss of capacity of the termination to carry the voltage, and a resulting voltage drop.