I think you need to sit down with the lender and both agree that this mortgage is unsustainable. The absence of your ex makes it even more difficult. Presumably, he won't agree to sell the house or engage at all with the lender.
So what have you got to offer the lender?
You can agree to surrender the home to them.
They will need to get a repossession order against you and your ex. You will agree not to challenge this. In fact, you will support it.
They will get the order and you will agree to maintain the house and keep it in good condition while they try to sell it. This maximises the selling price for them.
In return, they will agree not to pursue you for the shortfall. I presume that they can do that while retaining their right to pursue your ex. Although as he has left the country, they probably won't bother.
There is no advantage to you or to them in your going bankrupt.
They might demand that you pay the €10,000 over to them in exchange for agreeing not to pursue you.
If you like the house, is it possible that your new partner might buy it in his sole name for the current market price?