Well it depends hugely on the subject, and tutors have a lot of autonomy so even within a subject there are going to be considerable variations, so please don't take this as the only answer as it's only based on my experience and those of people I know.
The essay is still core to a lot of tutorials, but they tend to be interspersed with other things too. One examples is that students are often asked to give presentations and make a set of slides to support their presentation rather than writing essays . Other tasks are going to vary depending on what the course is so it's hard to generalise (e.g. for some subjects a book review of a canonical piece of scholarship; for another it might be a task focused on source selection or close analysis rather than essay-writing.) There is also more assessed coursework than back in the day (though this may change because of AI - sadly I suspect that in all universities, there will be a return to closed book exams). I know of some more tutors who offer students the options of things like museum/gallery/archive visits or reading groups, either as a supplement to a tutorial course or in lieu of a particular tutorial week.
Centralised teaching: again depends hugely on the subject, but most Faculties will offer courses taught through central classes, either by themselves or in conjunction with tutorials. These may be a core compulsory course, but some Faculties offer specialist subjects which are class-taught (so students can then opt in, either because they like the subject or because they want a change of learning style). Centralised teaching would usually be a small class (e.g. 6-10 students) from different colleges, and the teaching style would not be essay-based but more discussion and possibly presentations, with perhaps written work due in at intervals during the course; sometimes it's team taught by a pair of tutors too.
I don't know if you've heard of Opportunity Oxford, which is a bridging course for some students from non-traditional backgrounds to help them make the transition to university study. They do a 6 week digital course over the summer before they start, and then they come 2 weeks early for an in-person session, which means they get to meet other students from similar backgrounds, as well as getting some extra support with academic skills. I think that helps a lot with the feeling of 'sink or swim' and also the perception that 'no one else will be like me'. That isn't self-referral, though - students are invited on the basis of the widening participation data that the university collects during admissions.
There's a lot more general study support organised by colleges which is open to all students regardless of whether they come from a socio-economically disadvantaged background. Some now employ a 'student mentor', who can help with the practical side of developing study skills and life skills, e.g. 'I don't know how to organise my week to meet all the deadlines' or 'I don't think my academic writing is very good', but also could be 'I'm struggling to manage my budget' - obviously this can shade into welfare support and so help people get signposted on if they need more specialist help. Quite a lot of tutors organise sessions for their incoming first years on academic study skills topics for their own subject, on things like 'how to approach a reading list', 'how to write a good essay', 'how to use digital resources in your studies'.
However, none of this is perfect. A lot depends on students being signposted to the appropriate support as well as being willing to take it, and tutors being willing to be inclusive in their teaching approach. I don't want to say that there aren't people who struggle and feel lost at Oxford - I'm sure there are. And a lot of people at Oxford struggle with imposter syndrome.