Highers are usually the 'equivalents' to AS levels, although universities realise that Highers are more difficult.
That's actually decent to get into Leeds with a conditional with only Highers, I do think you have other things like Open University courses etc. which convinced them maybe you're the exception and you could've gotten in without Advanced Highers.
Scottish university are one year longer because they start from Highers. To enter an English university without Advanced Highers is almost like early entrance to university.
For Leeds you can technically meet the requirements with
six highers (equivalent to six harder AS levels), but I mean Higher is basically a harder Year 12, so basically by entering Leeds with only Highers you're
skipping a year. I mean, Leeds is 92nd place in QS 2022, which is basically around St Andrews at 91st place. (
https://www.leeds.ac.uk/undergraduate-applying/doc/accepted-qualifications)
Maybe the OP is considering Oxbridge, UCL, Imperial College London, LSE etc. and these will need Advanced Highers.
For Oxbridge, (
https://www.ox.ac.uk/admissions/undergraduate/courses/admission-requirements/uk-qualifications) you will see that if you're capable then
three advanced highers, for Oxford it's AAB to reflect the fact that Advanced Highers are harder than A-levels. A in Adv Higher = A* in A lvl, B in Adv Higher = A in A level. Cambridge doesn't care and just goes A1,A1,A2 for A*A*A.
Oxford does need
5 highers, unless you're an exceptional case, then maybe they could let you in.
I agree with your nat 5 part, I think the OP should drop it (unless it's important).
'There’s a LOT on your plate. Too much.' It's not that much, it's basically three harder A-levels plus one harder AS level plus a harder GCSE, it's not too much when you consider loads of English students attempt 4 A-levels, and they're quite fine.