86 year old cooking on the stove, but there’s nothing in the pot. Is this a sign of Alzheimer’s?

Gut reaction...(and I seem to be having a few of them today)..
This woman should not be left alone.
The stove should be "disabled" if she is alone.
If you can not disable the stove totally then remove the knobs so she can not turn it on.
You should discuss this with the doctor as soon as possible but if it will be a while then you should report this to your supervisor (should do that as well) so that you have alerted your "superiors" to a potentially hazardous situation.
Unfortunately many people will only act after a catastrophic event. ("we" ..people tend to be REactive not a PROactive ) No one wants to admit that their loved one is declining or needs help.
But seeing what you are seeing in order to protect your client as well as the agency you need to report ASAP you observations. And if this is a decline since she was first evaluated for service then this is an indication of a decline that the agency should be made aware of simply because she may need more care than you are able to give. (24/7 not just a few hours daily)

I went through this with Luz. I found the burners turned on but only one was lit. The other was just hissing gas. That is when I removed the knobs from the stove.
She some other kitchen adventures. She knew that coffee in the pot had to be poured but she forgot the cup and poured coffee onto the counter, twice before she quit that. She forgot how to set the micro wave and blew up a cup of coffee.
She would drink the worcestershire sauce straight from the bottle until I hid it.
She had other strange things with food. Luckily I was at home with her. She could not be left alone, so when I needed togoto the store I would hire a companion to sit with her.

If you are a private hire by family, there is little protection for the lady or for you. You did not mention the type of employment situation. Licensed or accredited agencies require charting of work/intervention performed after each visit. Behaviors would also be charted and submitted to a supervisor. You would also be charting your hours worked and there would be a paycheck system that also tracks you work time. You have not clarified what your hire status is.
If the lady is capable and willing I would try to place a call to the adult children. In the course of this discussion I would gently bring up the issue. Nobody can legally prevent her from calling her family. When adult children live far away and an agency is involved in her care, they expect the agency to act immediately. They may also be in denial and deciding someone is over reacting to her "off" behavior.

Adult Protective Services will intervene, if notified. That will put the ball in everyone's court - any agency, family, you. Everyone will get on the same page.

In our area if a caretaker is known to have had knowledge of a dangerous situation, such as what you are describing, family and law can be very unforgiving. You "allowed" this to persist - unless you have documentation reflecting otherwise.

Agencies and families scramble to assign responsibility to someone for allowing such a dangerous situation to continue. In our community, news articles almost always name the caretaker as the person arrested or fined for allowing this to persist. This person may get relief if employed by a reputable agency, but usually the immediate caretaker is swept into the mess no matter who is finally determined to be at fault.

Additionally, the bad guy - in this case you- typically faces future legal and future employment problems. If you're not with an agency it's especially important that you remove yourself from this situation entirely. Call Adult Protective Services ASAP.

It's definitely a sign of something which you need to report immediately to whoever is responsible for your client's care. Are you in touch with anyone in her family, are you employed by an agency? - speak up as soon as you can, whoever it's to.

Please call the county.  She needs intervention for her own safety.   Plain and simple.

Three signs that a person can no longer safely live alone: 1. The begin to wander. 2. They leave doors unlocked where they go out or at night. 3. They forget what they are doing and leave pots on the stove to burn.

Probably these are signs of encroaching dementia. They are definitely signs that the person shouldn't be on their own.

Definitely this is a sign of Dementia. This woman can no longer be by herself.

DANGER ! Disable her stove no matter who you are and why you were there and even if she protests. Then get help.

Although this behavior can be caused by lack of sleep, meds, UTI, I would really tell somebody in charge because it could be dementia which most likely is but she needs to be check out by a physician.

In my twenties I had insomnia and I put my car keys in the fridge, milk in the oven. Finally went to sleep and when I woke up I thought somebody else did it. I came to realize that it was me because there was no body else there. I lived alone! The things we do when we don't get enough sleep. LOL!

Many, many families are in denial about how much care someone with dementia requires. In my opinion, APS is like the nuclear option. Some counties have great APS and others report them to be nearly useless doing little besides pointing fingers and judging living conditions.

"Son is out of state and will not help. Daughter has to work to support herself and is a few hours away." The sad fact is that most Americans are living paycheck to paycheck. Most Americans have not saved for retirement. Many Americans are choosing between putting food on the table and gas in the tank. The son and daughter may not be in denial but rather be struggling themselves to keep their noses above water.

I would document your concerns. Take pictures of the burned pots, popcorn, soiled clothing, etc. Show and discuss the pictures with your supervisor and come up with a plan. Your supervisor may decide APS has to be called. Before calling, I would want to know exactly what APS can do to help this woman.