Not sure what the snow conditions are like over the next couple weeks, but assume pretty good coverage.
The steepness resembles the chute on the Whitney main trail, but Shasta is longer and more sustained. There may or may not be a bootpack. There was none when I did it, but the snow was in good condition and my crampons bit well. There were a couple people who tried climbing it in microspikes and one with no crampons, none of them got very far up after the campsites.
Depending on the direction you take up, the steeper parts are at the Red banks and above.
Note also in my photos, the errant rocks all over the place, there is a lot of rockfall there, so bring a helmet, but more importantly, pay attention and listen for anything coming down (ie don't climb in headphones).
Shasta was an awesome climb, but it is a lot of gain in one day.
Below is my report when I climbed it in July a few years back.https://www.14ers.com/php14ers/tripreport.php?trip=16226