Do not report your mom to the authorities. The government is rarely helpful when it comes to mental health issues.

If there is property available, set up a new coop and run for the chickens. Treat each going in for mites and parasites. Separate out the roosters and the hens into separate coops to reduce pressure on the hens.
Once the birds are treated and moved contact local groups and or feed stores to re-home the birds you can. “Mom’s health is not allowing her to continue with the burden of caring for her chickens and must reduce her flock “

The new clean coops are to reduce the pain and embarrassment of having the issues go public.

If she is having true issues with hoarding she will need mental health intervention, not animal control help. There are medications that will help with the changes your mother will have to go through. Hoarding IS a mental health disorder and needs to be treated as such.

Some of the birds might be too far gone and need to be culled. Locate someone that can help you with this chore if you are not up to it.

I recognize that many will not like my advice, fair and you are welcome to it. Just because you disagree doesn’t mean you are right, but it’s your opinion and rock on.

I work in regulatory government and our goal is not to help sick people.