During the HR screening, the recruiter asked about my current location, my legal working status and visa situation, whether I have valid work authorization, and my availability or flexibility for relocation or remote work.

Very poor/unprofessional conduct for a technical (data structures/algos) interview. For one, the technical interview was conducted by the RECRUITER, not a software engineer. Therefore, the interview was less about your problem-solving approach and collaboration, and instead was simply if you got it right or not. The interviewer asked a jump game question, and while I got the O(N) approach, I was unable to get the O(log(N)) approach. I stated that I think a binary search algo would work, but was unsure how to move about the pointers (This was after I tried several different methods to figure out the approach). This part would be where the interviewer would step in, and maybe offer some guidance. However, since I was not interviewing with an actual software engineer, the recruiter was unable to help. After some time (about 40 minutes in, after repeated attempts to engage with the interviewer, to make this closer to a professional technical interview), I stated that I couldn't get the optimized approach (I wrote out a rough implementation of binary search). The recruiter then asked "Ok, so is this your final implementation?". I stated that the linear approach would work, but the optimized approach wouldn't. (At this point I am not even sure if there was an optimized approach, as I exhausted every possible method I could think of, and also got no feedback from the interviewer.) She said that she would take this back to the hiring team. At this point, I don't know if she understood a lot of what I was saying, and was simply looking for code that would give the correct output when I ran it. I want to make it clear I don't blame the recruiter for this unprofessional interview. I am unsure if this is how they always conduct their interviews, or if they simply did not have any software engineers available to conduct it (and in that case why wouldn't they reschedule?) Again, I don't understand how they can schedule a coding interview without an actual software engineer as an interviewer. Don't waste your time applying to this company.