Service Dog Denied As Accommodation For Job? Was This Legal Under Ada?

I was supposed to start work at a company (located in USA) today and had received my first day details a week or two ago. I had brought my service animal to the interview appointment and no issues were brought up and it all went smooth. Upon hire I had put accommodations in which I was told would be sent over to the job facility I was working at and either the week of working or on my first day would either receive an email or phone call to follow up about my request. I sent a follow up email the day before as I hadn't heard back and assumed that it was something that would be handled on day one of the job as that was specified in the email as a possibility.

I arrived to work and was allowed access to the building, but told they had received no record of my accommodation request. The manager called someone in from HR and we all sat in an office. I showed them the emails, which checked out as valid and HR said they were going to 'investigate' what happened. I was then told I could not work at this facility as it was deemed 'unsafe' for the dog and 'too high of a stress' for me as a disabled person (he's medical alert as I get seizures) and told 'I need something calmer' but I was familiar with the environment as I worked in very similar job positions before getting my SD. It's a warehouse position that requires you to go into a freezer for a certain amount of your shift. I wasn't sure why they couldn't find a position outside of that portion of the job or why my service animal couldn't be left outside of the freezer, or why I couldn't spend less of the required time in there. I was under the impression I was going to be stocking shelves or maybe working on a conveyor belt, a job that still would be helpful but that I could still work with my accommodations. But they just said he could not be accommodated at the facility and they are gonna try to place me elsewhere.

They then backtracked saying they might not be able to find me any placement and that the other warehouses might deny my request same as they did. They also asked for paperwork for my service dog. I was confused as here in the USA there is no paperwork required to be shown, I offered vaccination records but that wasn't what they were looking for. They also were asking for medical records or doctors notes explaining my disability? They kept saying to upload paperwork in the system. Which I was very confused by, is this normal? They kept emphasizing that "the job is just too hard to do with a dog attached to you" I was super anxious and tried to explain he does a lot with me and is very capable but knew they weren't going to budge so I just nodded my head, stopped arguing and agreed, knowing I would be able to do something about it later as they admitted they've never dealt with a person with a SD before.

They ended up sending me home an 1 1/2 into the day and only paid me for that time. They said I'm on unpaid leave until they can investigate what happened and also until they try find me a new placement "if possible" I was embarrassed, felt isolated, and very frustrated at the way all of this was handled. Am I overreacting, I have never had something like this happen before. Is this grounds for a lawsuit? If so, what steps should I take?

I reported it to the corporate HR, ethics hotline, and kept records. I also do have a voice recording of my service animal being denied the access. Any advice on how to handle this? Should I wait and see if they find me placement elsewhere first before taking things any further? Any advice will help.