Ok, a couple of things beyond doubts:
The Buses to Aosta and Courmayer depart from the parking lot in front of Turin's PORTA SUSA station. So get off the train at Porta Susa.
Trains do not sell out, but discounted tickets are capacity controlled. Because of Covid Trenitalia has stopped selling their cheapest tickets, called SuperEconomy.
Discounted tickets come with restrictions: usually it's no changes and/or no refund. Nobody pays the top, walk-up fare in advance online, but it will is always displayed both on trenitalia.com and italotreno.it. This way you can see at a glance the price of flexibility.
Freccia-something is the marketing name of Trenitalia's high speed service. "Marketing" because the Freccia-bianca trains are not bullet trains according to the new railway benchmarks.
Trenitalia's high speed Frecciarossa trains are faster and less tilting than Italotreno's; but Italo is cheaper, the on board complimentary wifi is easier to use and their staff is forced to be polite. Some could even be actually happy to see you. Trenitalia's staff hates us all, but they hate you much more than me.
June 12 is the day of the seasonal timetable change all over Italy. Before Covid, on the 13th of December, 2021 you would have been able to see online all the train schedules up to the 12th of June, 2022.
Now, if "mid June" means "after June 12" you'll have to wait early May before seeing the full schedules. I'd make a first check on April 1, the State of Emergency has been postponed till March 31.