Do Ubers run from Trieste to Koper, in Slovenia? Taxis? I worry that going over national boundaries could complicate things.
I took a taxi doing exactly this in 2019. No issues.
In case you are doing the same, I did this as part of a rental car shuffle. I dropped off, taxied and picked up in Slovenia. It went fine.
Taxis and NCC - point to point drivers - are your private transfer options in Italy. Uber is essentially only a limo company in Italy and they may be able to help you with this transfer but it is not the same as Uber in other companies.
There is also a twice a day bus but if the taxi option is available it's certainly easier if not cheaper.
Have a great trip,
=Tod
We used daytrip.com for 3 people going from Venice to Rovinj, Croatia. It was more expensive than the bus but also more convenient and comfortable.