MIL is in a nursing home and is experiencing severe delusions and confusion for about two weeks now on and off. What can I ask the NH to do?

I am surprised, all other things having been normal, and MIL having entered with all these changes that the neuro-psyc eval wasn't done to assess if there is dementia, evidence of undiagnosed strokes, and etc. I think it is the medical system having let you down more than it is the nursing home, which sent her for evaluation. While the system did the routine things, they didn't go further, and one wonders if this is the case that people on Forum so often give anecdotal evidence of--a 97 year old in which the system, now overwhelmed with Covid on top of everything else--a system saying "Well, she is 97".
I would be about where you are now, feeling hopeless and helpless; guess my next step would be a request for Neuro-psyc eval. At the very LEAST there is going to have to be some sort of medication cocktails that can keep your MIL relatively comfortable.
And do request a retest on that urine thing. Sudden changes are so often that. I understand she has tested negative, but be certain they did a C&S. Some of my infections didn't show in just a U/A. Be sure they do a culture and sensitivity.
So sorry you're all going through this.

Certainly with those symptoms, was she screened for dementia? Has she displayed any other unusual symptoms? Delusions and confusion are typical dementia symptoms but usually don't come on that fast. Cognitive issues usually show up first with dementia along with difficulty in performing normal daily activites. UTIs can also cause these symptoms but you say the tests were negative. Meds interaction is also a cause along with vitamin deficiency. Did the CT scan show normal brain shrinkage for her age or maybe indications of mini strokes? Were they only looking for a brain bleed and maybe miss abnormal shrinkage? Did the bloodwork look for any AD/dementia biomarkers? There can be many reasons for her symptoms. If it hasn't been done, I would have her screened for dementia.

Just to cover all bases...if your MIL is on any thyroid meds: I recently had a relative experiencing weird symptoms and it turned out to be her thyroid medicine. She had lost weight, which caused her to be overdosing on her meds, which in turn created the weird symptoms of confusion and memory issues, which in turn caused her to lose more weight because she didn't remember to eat or not feel hungry, etc. in a loop. Many women are on thyroid meds, so if your MIL is as well please have her dosage rechecked that it's appropriate for her weight.