O2E Brands interview questions

Application was submitted online. The application package consisted of Cover letter, resume and additional information on a very similar, recently completed project strategy and implementation. After a month and a follow up email (understandably these days) I finally received an email from an HR specialist for an initial interview that was scheduled the following day. Interview went for 30 minutes. During the interview, first I was given an overview of company culture and then I was asked the question if I could do what they were hiring for, which we then discussed in great details as I have just completed a very similar project. HR specialist reaction to a lot of things I said was "I love it!", "great you mentioned it!", "that's exactly what we are looking for!". Then was my turn to ask questions and we talked about the main topic of most of the media pieces I found and watched while researching the company - the most important asset of the company - its people. At the very end of the interview, I was asked what was my expected compensation to which I responded that at this stage of the interview process it was important for me to see if this was a good fit first, cultural as well as project/team specific. The HR specialist insisted on the number. I've asked what range they had in mind and then mentioned the range I earlier researched on PayScale which was slightly higher (my lower end was equal to their upper) also mentioning that if this is the right fit then I am sure we could come up with mutually agreeable compensation terms. Then we discussed the next step of the interview process which was going to be an interview with the Hiring Manager within 2 days. I was also told that they were impressed with my application and I was their top pick among other applicants. Then a week has passed, again understandably these days. After another follow up email I got a reply that they were trying to up the budget to meet my compensation range. From this point on the conversation went somewhat strange. For some reason the compensation question which was only discussed briefly became a show stopper. I suggested we continue the interview process to meet with the Hiring Manager and the team while this side of things being sorted out however I received a response that they don't have a budget for what I was asking and after I've responded that I totally understand budget constraints, I received the final email where I was told that the top end of the budget was lowered even more and now they can't afford someone at my level at all.