Extraction of Inflation Expectation from bond yields
Yes, the number you give is an approximation. If you wanted to calculate the true economic breakeven, you would need to include the effect of the lag used in the indexation process (which includes known inflation information), coupon cash flows, seasonality of inflation, etc. If there is a maturity mismatch, then you would need to decide how to handle that as well.

However, the deviation between the economic breakeven and the approximation is normally small. In fact, the market convention is (or at least it was) to ignore compounding and just use the spread between quoted rates.

You would need a full fixed income pricing suite to calculate the true economic breakeven, so a course would stick to the approximation.