Advice needed! Caring for my grandma is killing me. What do I do?!?

I'm 29 y.o. & am the sole caregiver of my 86 y.o. grandma w/dementia which was put on my shoulders after my mom's sudden passing in early 2020 (we have no other family)...Over the past year, grandma's mental faculties have declined & she began exhibiting signs of dementia which have gotten worse over time. Since Sept, there have been 3 incidents (wandering & such) that ended with her getting admitted to a hospital after 911 was called due to safety concerns. It is now very clear that she can no longer live alone.
Unfortunately, I don’t have the ability or the resources to take her in so, over the past 5 months, I’ve been desperately looking for LTC placement...Sadly, there are several hurdles that have made it extremely difficult find placement (I've contacted 32 facilities in my state so far with no luck): not only does she not have any assets or income (other than monthly DTA payments), nor does she have SSI, pension, retirement savings or Medicare. Her only way to pay for LTC would be MassHealth (Medicaid). Additionally, she is unable to speak English so the language barrier has made it even harder...After the 2nd wandering incident in Nov, her landlord had apparently served her with an eviction notice on giving her a little over a month to vacate; however, since the notice was in English, she didn't know what it was and forgot all about it until she finally showed it to me on 12/23/21. She is now awaiting a hearing to be scheduled regarding the eviction…Long story short – not only is she not able to vacate her apartment due to the fact that she is still currently at the hospital because they don’t want to discharge her to go back to living alone (admitted for the 3rd time on 12/25) but also, she has nowhere else to go if LTC placement isn’t arranged.
I’ve tried almost everything – our state’s Family Caregiver Program through the Executive Office of Elder Affairs, local aging programs, endless research; even the Case Manager & Social Worker at the hospital where she's admitted have done absolutely nothing.
To make matters worse, she is the most cynical, negative, conniving, nasty, ungrateful person. She grew up during WW2 and lost her entire family in the war so she was put in an orphanage until her adolescent years. The highest level of education she completed was 3rd grade; that plus her innate pessimistic personality and all that life has thrown at her has made her into an impossible person to deal with…She loves to play victim and always lies about everything. When she doesn’t get her way, even for minor inconveniences – for example, she calls me during my workday to tell me that her computer “stopped working” (she accidentally hit the wifi button & turned it off) and expects me to drop everything and run to her to fix it (she doesn’t live close). If I don’t, she starts spewing hateful things such as “I’m going to kill myself then write a note and blame it on you”, “my death will be on your hands”, “your mom never wanted you” and so on until I break and give in to her demands. With the dementia, it’s gotten much worse…She has absolutely no idea of the things I have to do to make sure she’s taken care of like doctors’ appointments, paying her bills, making sure her annual recertifications for housing/health insurance/SNAP/etc. are in order, buying groceries, arranging for aide/nurse visits, ppwk and so on.
I am so exhausted and stressed that my health is taking a toll. I just recently got engaged and I want to live my life, grow my career and start building a life with my fiancé but I feel like I’ve lost the ability to feel happy. I resent her because I feel like I’m wasting my youth as she sucks the life out of me. I don’t even want kids anymore because I feel so depleted.
I’ve even thought about changing my number and just walking away…Is it possible for her to become a “ward of the state” while I am still around?
I just know I won’t be able to keep keep running on empty like this forever...