There are futures contracts referencing treasury bonds in many countries. Most (U.K., German...) are very similar to the U.S. Some (Australia, South Korea) are a little different. You seem to be asking about U.S. treasury futures.
When such a futures contract is defined by the exchange, it lists some underlying bonds that can be delivered, and a conversion factor (CF) for each bond. The CFs don't change during the life of the futures contract.
Simplistic approach to decomposition: run someone's model that finds today's cheapest to deliver (CTD) bond.
Value and risks of the futures contract = value and risks of the CTD bond / conversion factor of the CTD bond.
The disadvantages are:
1 you don't see your exposure to the spread between the futures and the underlying cash bond, which can sometimes widen dramatically (like it did in March 2020, for example).
2 day to day, the CTD bond may change, and then the value and risks of the futures contract may (or may not) jump.
More sophisticated decomposition: have your model output weights for each underlying bond based on the probability of each becoming the CTD; and decompose the futures into the basket (weighted sum) of the underlying bonds, and the idiosyncratic spread between underlying bonds and the futures.