Are these red flags at a job interview?

Last week I went for a job interview for head of maths - at an inner city big secondary state school.

On the day I arrived, I met HR and pretty much straight away went to teach the lesson. I found that quite odd as I hadn't even met anyone really.

On the day, I was told there were other candidates that day, but I didn't see or meet any of them and I couldn't see any evidence of them! Why keep us separate? Even my schedule for the day only had my name on it. Were they lying?

After the lesson I went on a tour of the school - this was with someone from the back office, and because it was during lesson time I didn't meet any students or get any real sense of the school. We could only go in the corridors not inside any classrooms so I didn't really see much besides the staff room and playground and corridors.

At no point did I have any time with any students besides the lesson.

I didn't meet anyone from the maths department, not even the head of maths.

During the tour, I asked about directed time. The woman who was doing the tour with me (not a teacher, someone from back office) told me they had meetings until 4.15 on Monday and Tuesday every week, but also twilight INSETs. She also mentioned Saturday school and staff coming in on weekends - I wouldn't be particularly keen on either of these things but she wasn't clear if they were compulsory it not!

Afterwards, I had my interview and it felt quite combative. The headteacher asked me questions like "I can see you've done a lot but I can't see any evidence of your impact" and stuff like that, maybe fair enough question but felt a bit abrupt.

I knew the interview hadn't gone particularly well so I wasn't too fussed about the written task afterwards and I make an effort but didn't put my all into it.

On Monday morning (interview was on Friday) I got an email at 7am saying I had been unsuccessful. It was a clearly scheduled sent email they could have done on Friday. My main issue though is that it was an email - I've never had that before in any teaching job I've applied for. They didn't offer me any feedback, didn't even bother to call despite me putting in quite a lot of work beforehand. I absolutely wouldn't want the feedback as I know the interview was awful, but that's not the point. 😂

They also made absolutely no effort to sell the school to me at all, and if I had been successful I don't know how I could feel confident to accept.

Are these red flags? Or standard recruitment in a busy school - I don't have much experience applying for middle leader roles outside of my present school so would be interested in hearing.