How does one function while living with their elder's continual confusion?

You may want to bring this up to her Dr. To me this is an anxiety and there are meds for it.

In your mind, you are not confused.

In her mind, she is not confused.

She cannot enter your brain, and you CANNOT enter hers. You don’t need to try to “straighten her out all the time” because she can’t be straightened out. Her mind no longer shares your map. Think of your interactions as parallel roads that will never intersect. If she is willing to listen to you, tell her stories about news events, family members, anything that interests her.

If she is able to initiate comments, let them go if she’s comfortable offering them. Be comfortably and pleasantly silent and let her talk. You don’t have to answer or interpret or correct.

If she is sometimes quiet and peaceful, it’s OK to let her be.

I mourn frequently about the loss of my LO’s razor sharp comments about the world when she was well, and I’d give anything to have that back, but as long as she’s safe and peaceful and I respect and love her, I’m doing what she needs.

I get frustrated with this too. Sometimes I just don't answer, which is a bit mean, but the silence can sometimes redirect. The same questions day in day out can really be wearing.
My own cognition has really suffered since I started caretaking so I understand your frustration.
My mom is physically in pretty good condition as well, but often confused. It's a difficult situation to be in isn't it?
Too bad there wasn't a way to recharge patience banks somehow! My is depleted.

Watch Teepa Snow videos, which you can find on Youtube. She explains Dementia and AD very well. Then with the new understanding you gain from knowing your mother's brain is broken, you remind yourself of this in between taking lots of deep breaths! Of course, I know that isn't really an answer since there is no way to not feel like your own brain is being twisted up in a knot.
There is always respite care or placing her in a facility. It gets worse, so even if you think you can handle it at this point, you may still want to look for a facility for when things are really bad. It's tough, I know.