I think I’m about to buy a Velotric T1 ST Plus which would be my first ebike.
The manual says to store it indoors at a temperature of 50°F to 77°F (10°C to 25°C). However the location I actually have to store it in is in an uninsulated shed that will probably reach 120ºF (50ºC) in the summer in baking sun, and below freezing in the winter.
Is this going to kill the bike or its battery?
No not removable.
If I buy the bike I will be sure to charge it overnight and not baking in the sun
Keep in mind you will want the bike/battery itself to be at a safe temperature before you charge it, not just the temperature of the air around the bike: It will hold heat or cold for longer.
You could use a thermometer but just feeling if it his hot/frozen to the touch should be good enough.