Can I get paid for taking care of my aunt?

This is exactly what my cousins were trying to force me to do. I stayed with aunt for a week and some weekends and knew that I couldn't take this on. No one even mentioned pay.
I suggest you rethink this. You have your own life. Don't do it.

There are many ways to care.
Being your Aunt's live-in caregiver is not the only way but this is your decision.

Was this always an expectation? That you would care for this Aunt? A long held plan & considered decision?

Or more a swoop in during a health crises reaction?

Take the time to think & plan.
Find out a time frame if possible.

A 2 week stint you will be glad you did VS 6 months of no pay & no way out. Big diffetence.

Being a live-in fulltime caregiver can be a rewarding role. But it comes with consequences. To your finances, job, maybe to your marriage too.

Why are you against a skilled care facility? The caregivers are professionals who are trained to help elders like your aunt. You need to visit some before you decide that they are torture chambers where aunt would be mistreated.

Please don’t be so willing to sacrifice your own family and perhaps your marriage when you seemingly know nothing about modern nursing facilities in the USA.

You can't have it both ways: keep your marriage and family intact or orbit around your Aunt for who knows how long. You can consider moving her to hospice near you, but if you aren't her PoA and she' not incapacitated, then she still makes her own decisions. But she can't assume you into this role and you shouldn't take it as it stands. You, your hubs and your family is your priority.

This doesn't mean you don't help your Aunt, it's just that "help" in it's current form is not working. Caregiving has to be on the caregiver's terms or else that person burns out (and maybe burns out others, like hubs and kids). Auntie will have to settle for a different arrangement if you help her. You need to insist on being assigned her PoA to agree to this. She should create a POLST and a Will, if she is still cognitively able. Otherwise she will wind up being a ward of the county with a court-assigned guardian, which may not be the worst thing. Our family had a good experience with this and it was a blessing, even though it wasn't perfect.

To answer your actual question: you can only get paid from your Aunt's funds at this point, since she's in hospice which is covered by Medicare. The state will not pay you.

She needs to be placed, it is time, giving up your life and family makes no sense.

Your Aunt has lived a long full life, don't give up yours for her, your family must come first.

You only have 1 life, don't sacrifice it for another.

Nursing homes are not what they were 50 years ago, have you done any research? I would. If she cannot afford to self pay, she can apply for Medicaid.

Time to take care of you and your family.