Perimenopause is a decline in fertility, not the end of it, and the two get collapsed together constantly.
What actually happens is that ovulation becomes erratic. Some cycles you ovulate, some you do not, and there is no reliable way to tell from the outside which kind of month you are in. A cycle that arrives at day twenty-one one month and day fifty the next is still capable of producing an egg.
The hormone therapy point, said clearly
Standard hormone therapy does not suppress ovulation and is not contraception. Women are given it, told their symptoms will improve, and reasonably assume the pregnancy question is settled. It is not, and this is worth raising directly at the appointment if nobody raises it with you.
The combined hormonal coil is a useful exception, because it provides contraception and the progestogen half of hormone therapy at the same time. That is a conversation worth having if both things are on your list.
The rule most guidance uses
Contraception until twelve consecutive months without a period if you are over fifty, and twenty-four months if you are under fifty. If you are on hormone therapy and no longer having recognisable periods, the usual advice is to continue to age fifty-five.