How do Schnorr signatures impact coin selection and the utxo growth? Will Schnorr signature incentivise different practices in coin selection? How do they impact the utxo set in the long run?
Yes, Schnorr signatures are generally slightly smaller than ECDSA signatures. This is due to their more efficient encoding that takes only 64 bytes instead of 72 bytes.
A comprehensive Coin Selection algorithm should therefore e.g. prefer an input with a Schnorr signature at high feerates and should prioritize using up non-Schnorr inputs at lower feerates to minimize costs.
In combination with the signature aggregation, we may generally see more consolidation and batching transactions, and may additionally see a market for creating multiparty transactions as combining multiple transactions will lowers overall cost.
I would expect the UTXO set to shift from old style UTXO to newer, more efficient formats over time, but whether the growth of the UTXO set would be impacted and how, is difficult to predict.