I would probably do one of two things.

Safer option: Transfer stores. SM is not going to change. Get out sooner rather than later.

Bolder option: Chat up your DM when they’re in and mention you were looking to be a SSV and play dumb. But going over your SM’s head is basically a shots fired kind of thing. (I did it once concerning our lack of breaks, was promised I wouldn’t be retaliated against, and I had a write up the next day.)

Only working one kind of shit isn’t entirely wrong. I only do mornings. That’s normal. People don’t and shouldn’t be forced to work shifts they don’t want to - especially if out of their availability. Keep that in mind for yourself if you don’t want to do closing or whatever.

That being said the “stringing along” thing is really scummy. Honestly? Speak to her. That’s about all you can do.

When you're hired you fill out availability. When I was initially hired I was only able to open because I had a second job that started at 7pm. There are some employees that have never opened because they are in highschool. Everyone has different availabilities and you may be able to say favorites on not being promoted but you scheduling isn't it. I exclusively did opening now I switched to closing because my other job is in the morning. People might have kids so have to be off at a certain time. People might have school so have to work later in the day. People have religious exemptions. I understand your frustrations but you aren't even a shift so you have no idea what conversations went on with those people or their availabilities. If you don't want to work a certain shift change your availability or transfer to a different store and tell that SM that you don't feel you can climb the ladder at your current store and just want more opportunities.

Honestly, this isn’t favouritism. Why does an opener have to have a disputed shift pattern? When you’re hired, you get asked about the hours you can work & they’re clear about start/end times. You could ask only to be an opener/closer - the trade off is that you might not be able to get as many hours as you want/have limited opportunities for progression.

If you personally hate closes or something, you can change your availability or days you work. You literally get to pick and choose the hours you work (I’d give some advance notice about changing availability to be considerate though). That’s not favouritism & working closes isn’t a punishment anyway.

Also, you aren’t owed being a shift. Your SM can pick who she wants to be a shift, it’s her store & she’s ultimately responsible for it. Why shouldn’t she pick people she knows she works well with? Why do you care what hours other people work? It sounds like you aren’t communicating well with her. You could ask for a coffee chat and have a frank discussion about if she’s thought about promoting you to SSV, why/why not, what qualities she personally is looking for in her SSVs, what you could do to develop whatever she wants & a realistic timeline you can hold her to. The worst that can happen is that she can say she doesn’t see you as a SSV in her store, in which case you then get to think about if you’re happy to stay as a barista, happy to stay as a barista but want to change your hours/days (which she may she can’t accommodate) or if you want to apply to be a SSV elsewhere.

It sounds like there’s a lot of resentment building up and not a lot of communication.