So some advice :
The Gotthard Base Tunnel is indeed closed and all trains run via the old scenic line (1h longer) but it isn't on your route at all.
You are looking at the Bernina Bus from Lugano to Tirano (10:00 - 13:00). It can only be booked here through the railway company (add Eurail as a discount during the booking process) : https://shop.rhb.ch/en/bernina-express/
There are 7 seats left on the 2 buses so do not wait to book (17 CHF). Where are you trying to book ?
From Tirano there are hourly regional trains to St. Moritz : reservation-free with pull-down windows. There is also the Bernina Express at 14:24 but it does not stop in St. Moritz itself, only in Pontresina -> 26 CHF seat reservation for the panorama carriages but there are reservation-free regular carriages at the front.
imho the hourly regional trains are better for pictures, less crowded and the way to go. :)