What do I do with my caregiver borrowing money from me and convincing me to add her to my checking account to pay bills?

You are are coherent and obviously able to use technology otherwise you would not be able to post here on this forum. So, I'm going to assume that you are in your right mind and it's not so riddled by dementia that you don't know what day it is.
There's a wise old saying that apparently applies well to you.

A fool and their money are soon parted.

You don't put some agency hired caregiver's name on your bank account because they're going to write checks. Why should the agency she works for reimburse you? She didn't steal anything. You put her name on your account and that turns it into a joint account so that's her money as well as yours.
As for the loaning of money that she isn't paying back. Unless you've got proof in writing of a loan and when it's to be paid back, you didn't loan her anything. More likely than your agency caregiver committing a crime, is you were probably in a relationship with her that went beyond the professional caregiver/client one. And then she screwed you on the money.
I truly think you would do well to petition the probate court in whatever city/town and ask them to appoint a conservator over you and your finances. They have to answer to the court periodically so no one will rip you off.

You apparently added a "caregiver " to your account. Go to your bank at once and remove her name. Then go to see an elder law attorney and work to get this ironed out. You have posted about this some time ago, and apparently it is still going on. You need to see a Lawyer, or contact APS to open a case for you NOW.

Could this be a case of financial abuse? Sounds like it was all caregiver's idea and there was some convincing involved. My DH is a signer for an elder and he's fine with it because it makes elder feel better to have him involved (even though her financials are relatively simple). I, on the other hand, do worry about this arrangement because I fear that elder will forget she wanted this in the first place and/or someone will convince elder that her money isn't being watched or that my DH needs to be "watched." My DH is as honest as they come, but having to prove that would be gut-wrenching and time-consuming. Putting someone else on a bank account might not be a good thing for either party (depending on the people).

https://www.agingcare.com/questions/if-my-caregiver-wants-a-loan-and-doesnt-repay-it-isnt-her-boss-bonded-463750.htm

You asked a similar question a while back. We answered you then that loaning your aide money was not wise and that the agency was not responsible to pay it back.

Do you have any family? If so you need to get them involved. You also need another aide. As said before, its unprofessional for the aide to ask for a loan and have anything to do with a clients finances. I would call Adult Protection Services and ask if they can help you get out of the situation you are now in. I believe that you should also tell the agency what has happened. This aide should not be working with Vulnerable adults.

I know you may be embarrassed by all this, but you need help in reversing it.

I’m sorry you gave this person access to your money. Clearly the person didn’t deserve your trust. You’ll likely never get what you’ve lost back, but take steps immediately to stop it from happening again. Do report it to her employer, they should know what a dishonest person they hired

Not theft. Sounds like you gave her Carte Blanche to your account.
Remove her from your account NOW!!
Change all passwords that she has knowledge of.
Any money you “loaned” her is probably never going to be repaid. Expensive lesson. You can try to recoup the money IF you had the loan written down with the particulars as to how much and when the loan was to be repaid. But unless it was a large sum the lawyer will cost more than you would get back

Why would her employer be responsible for your bad decision? Most agency contracts state caregivers do not do finances.

If you have a Social Worker, see if you can get a financial fiduciary.

No, the agency is not required to payback money that you gave her access to outside scope of job responsibilities. But you can file a police report for theft, although you adding her to bank account complicates things. She could say you told her it was ok. Call the police to find out next steps.