When you say that “strata” says it is not common property, did you mean the Executive Committee or the Owners Corporation? Did you apply in writing and get a written response from the above stating that you are not dealing with common property?
If extending this pergola means attaching any new structure, fittings etc to the outside wall, then you are working with common property. The outside wall is common property, even if the pergola was not deemed to be common property.
Get any permission in writing from your EC/OC.