According to the lawsuit, obtained by TMZ, the singer-songwriter and actress/model purchased the Encino house through a trust in 2019 ... but now claim the place is riddled with problems that have forced them to get the hell out.

The biggest problems, they claim, are mostly with the waterproofing around the deck and spa area, not to mention alleged mold issues that they say have rendered the crib "virtually unlivable in parts."

The lawsuit -- which was filed by a trustee of Nick and Priyanka's trust -- says the house is not only "dangerous from a health perspective to occupy" ... but will also cost the couple a ton of time and money to fix. We're talking millions of dollars here.

The exact amount of alleged damages is unknown, but they're saying the damages are north of at least $2.5 million ... and the suit includes some photos to back up their claims. We have some of those shots here -- but it's hard to tell what exactly is depicted here.

The photos are in black and white, and seem to be scanned ... so the detail isn't great.

Anyway, as for why the lawsuit's dragging on for so long ... the trustee's lawyer Fred Fenster told Page Six, "It’s like everybody who put a pick or a shovel in the property is going to be involved, and it’s going to be up to the builder to decide and prove who was responsible for the defects." We should note ... other lawsuits have been filed over this situation -- with a lot of different parties involved suing each other, but no one is suing Nick or Priyanka, specifically. In other words ... there's big confusion over who's to blame.

Now, a source with direct knowledge tells us Nick and Priyanka are very disappointed with the building issues, and with the house still currently under repair ... so nobody is living in the house at this time. Obviously, they've made other living arrangements in the meantime.