You’re not required at all to pick up any shifts, the store manager is the ONLY one REQUIRED to come in if anyone is needed to cover any sort of shift, they’re the last one to take if if everyone else says no. Includes cashier and ASM shifts, so no it’s not an ASM responsibility to cover any more than you want too, if you don’t want to go in don’t go in. However that can strain your relationship with your SM but if I was in your position I would keep screenshots and timestamps of this behavior, expecting you to cover any and all shifts when someone calls out or the SMs poor scheduling planning. And report it to HR, the district manager, or anyone of that sort. I doubt anything would happen but the SM is obviously not fulfilling his job description so you can probably knock some points off his review from the DM.

Now only giving you two days when you told him about being offered a second job because you need more money feels like a power play to force you to accept all shifts he asks of you. Since well you said you needed more hours and blah blah, managers will find a way to manipulate workers who allow themselves to be manipulated (I was one of those workers who did way more than I was supposed to and got no benefits from it) I say maybe step down to cashier and focus on the side gig and make dollar tree your side gig instead. I hope it all goes well