Does anyone know the steps to take to get paid to care for a family member?

I agree with MACinCT, do not quit your job. Those who have quit have said they had lost a good income, seniority, lost paid sick days, lost paid vacation days, no longer adding to a 401(k), no longer getting profit sharing, no longer putting payroll deductions into Medicare and Social Security, the list goes on and on. I understand this is not an easy decision.

Please note that your Mother will eventually need around the clock care. Therefore you will be doing the work of 3 full time caregivers per day [who get to go home after 8 hours].

For myself, after my Mom had a serious fall, she zoomed into last stage dementia. The best thing my Dad and I did was place Mom in a nursing home. Dad was able to visit daily. Mom needed a village of professional seasoned people to care for her.

Consult with a Medicaid Planner for her state. She may eventually require Medicaid for LTC and many states have a 5-year look-back period. It is very easy to accidentally mismanage their finances in a way that disqualifies or delays their ability to receive this aid.

If your mom has "suddenly had a huge decline in mental status" this may be a sign of a UTI, so I'd get her into the Urgent Care soon to be checked. It can be treated with antibiotics, and you'll need to be vigilent against future ones, which are extremely common in elderly women. With ALZ she will be less or totally unable to express to you what's going on with her body.

As far as getting paid is concerned, here's an article from this very website:

https://www.agingcare.com/articles/how-to-get-paid-for-being-a-caregiver-135476.htm

Your mother/parents can pay you to be a caregiver.
This should be documented so that the money you get is not seen as a gift but the money is being spent for her care.
The person that is POA or her Guardian would be the one to discuss this with.