How would I get from Marco Polo Airport in Venice to Trieste?
Use go opti shuttle
https://www.goopti.com/en/
Another recommendation for GoOpti. We used this wonderful service in 2018 from Venice to Ljubljana. We would definitely hire them again!
Or take the train.
Or take the bus to Mestre and take the train. It it a ride of under two hours, with no changes, from there.