Nico, ask what your FSH was and also what your estrogen was.
If it’s desogestrel causing this, your FSH will still be low (so you are not menopausal and still potentially fertile) but your estrogen will also be low….
My stupid male GP didn’t test for estrogen because he said the desogestrel would interfere with the result. Which is true. That’s exactly why we needed to test it

As for contraception, there are other POPs besides desogestrel which don’t suppress your estrogen so much. Levonorgestrel for eg…. Or norethisterone.
But also we are not very fertile in our 40s and natural family planning methods can work really well. Or condoms!