I'm sorry but the nurse is talking rubbish. Or at least scaremongering.
Only around 15% of women use HRT.
That's not to say 85% don't need it, but many women are still unsure about it and don't always seek help.
You don't need to think about HRT until and if you have typical meno symptoms. You're statistically very young as the average age of menopause is 51, although that is an average.
Ironically, HRT is the first line treatment for depression in peri and NICE states that women are not to be offered SSRIs as they are not effective.
Do you think HRT would make depression worse?
The Mirena coil is only one option with HRT. Some women love it, some don't.
Only a tiny fraction of women on HRT use the Mirena coil as part of it.
The depo injection you had is not in any way like HRT. It's a synthetic progesterone (and it will be interesting to see if your depression eases now you don't have it because they can be linked.)
I'd take no notice of the nurse, but you work on lifestyle issues like taking exercise regularly, eating healthily, cutting back or out alcohol and doing things like yoga, mindfulness etc which can help with mood.
Don't assume HRT is a 'must'. It's there is you need it.
One thing to think about is that with the contraceptive you have used so far, you won't know when your periods have stopped. If your depression started around then, it could be the hormones in it, or it could be you are already in early menopause and that's why you've had depression.
See how you are now when you aren't using depo.