Transformer Voltage Designation

Sounds like that the entity given the task of rating the transformers has kept to a given scale...that of KV...."11 kV/415 V (actually) but it is specified as 11/0.433 kV". Nothing unusual there.

Also, the KV labelled rating that differs from the physical winding ratio
("33/6.6 kV. But it is specified as 33/6.93kV")
may have something to do with actual operating voltage within a given temperature range suited for the geography the transformer is to be used in.
Perhaps the upstream source has an output voltage that sets the label value 5% higher than it's theoretical rating based on winding ratio and lablled accordingly,
The 5% difference you mention may even just be a "buffer" safety value.
If it's a value used for creating a safety buffer/margin-of-error, unusual to have the KV rating higher....perhaps the entity labelling the transformer made a boo boo
...is the transformer made in China down the road from you?

...you may have also answered your own question, "anything to do with tap position?"

...I don't know much about transformers, can I have your job?

when you say 415 actually do you mean that this is what you have measured or what you think it should be?

Open circuit voltages V loaded voltages do differ and the appropriate tapping points would help to achieve the desired output for a given load. The output voltage will vary with loading anyway and it is up to the engineer to find the correct compromise.