I do think some schools are better than others- it might be worth trying another school/setting before giving up on the idea of teaching completely? I moved schools this September, because things were getting untenable in my last job for a lot of reasons (some of them outside the school's control to be fair). That school had a range of unfilled vacancies in September, and there are staff leaving at Christmas. I'll be amazed if they are able to recruit replacements (again, it's not entirely their fault- expensive rural town, crap public transport etc means it's not an especially viable school for ECTs, for example).
In response to your questions:
Is this how it is now? Yes and no- as I say, I think some schools/areas have it worse than others. Some subject areas have it worse than others, and depending on the school you can have departments that really struggle and departments that are fine.
But there is a national teacher shortage and school budget crisis, so...
Do parents know? Parents know when it affects them specifically. Last year I'd speak to lots of parents in my tutor group who had concerns about the amount of supply. By the end of the year, parents were aware of how many teachers were leaving and did seem to have significant concerns. But a lot of parents didn't have a viable alternative, and so they want to believe the head when they say it's a temporary rough patch and things will get better.
But equally some kids are lucky and they happened to not have as many supply teachers, or their teachers weren't leaving etc. And their parents would be shocked when I'd say things like "oh there's no available maths intervention" or "we aren't running DofE this year due to staffing issues". So I assume some don't know.
Is it covid as everyone seems to think? I don't think it's solely covid- I think covid hasn't helped, and last year on top of everything pushed a lot of people to breaking point. But I think the CoL crises, the pressures on school budgets, and the teacher shortage which has really been brewing/happening for a long time have all come to a head. I don't think things are really going to get better without major changes that have nothing to do with covid.
How bad is it when hardly anyone knows me but pretty much everyone I spoke to offered me a permanent job? Well, it depends- my friend has just left a school (left teaching, actually) where he was the last teacher who could teach A-level Physics. I think they'd bite your hand off if you could teach physics at any level!
Equally, as I said, previous school had real issues recruiting. Couldn't get maternity cover in certain subjects for love nor money- we had non specialists covering effectively for a full school year. We had maths teachers leave at Christmas who couldn't be replaced. We had a few teachers leave at Easter, who couldn't be replaced, either- and when I say not replaced, I mean their posts haven't been filled by permanent staff still (according to friends who are still at the school).
There are lots of jobs currently being advertised in my county- including primary, for January or "as soon as possible" starts. This isn't usual.