Hi, I have POI and am on HRT. Its pretty much the same for any menopausal woman - the difference between whether you take continuous or sequential (so having a break for bleeds) depends on whether or not you are still having periods naturally - If they've stopped then you just take it continuously.
My periods stopped and I had over 12 months without them, so I take HRT continuously. I chose this mostly because my partner had a vasectomy so I could be free of contraception and I didn't want to go back to it, but really it makes little difference.
I wouldn't be so sure that HRT is better compared to the contraceptive pill - you are essentially using the same hormones just in different strengths. Things like Mirena are licensed for HRT or contraception so there's a lot of cross over.
Switching can also be more of a headache than its worth and bring up new symptoms that takes a while to settle, so if you aren't currently having any problematic symptoms you might want to think carefully about changing.
As you have POI, its probably worth asking to be referred to a menopause clinic or gynaecologist so they can advise you and check your levels are appropriate.