Id report him either to your Store Manager or District.
Starbucks is definitely a place of equality and there is NO reason for the ssv to not try to help the team. Even my manager is regularly on the floor helping and working. Definitely bring up that you've not been given the opportunity to be on bar the way you want to because sometimes its seen as a YOU thing but clarify it isnt!

He is not doing his job properly. Document every single thing that you see (date, time, what wasn’t done, if he never switched positions for you, etc) and once you have enough, have a talk with your SM. Have other partner do the same.
If SM doesn’t do anything, go to the DM.