Your engineer and/or architect didn't provided a "complete" design solution if the design intent was to create a waterproof space below the patio. Altering construction details from their design may limit their liability, so proceed with caution. If the design was intended to create a waterproof space below the patio, I'd go back to them and ask how their design meets that requirements. If it doesn't, it seems it's incumbent on them to provide a workable design solution.

Post the drawing and specs you have available.

Yes you need a liquid applied product. Hydrostop by GAF is one I’ve used a lot. Sounds like a tricky detail that should have been thoroughly detailed

"everyone seems at a loss for solutions"

That is not a good sign, and crowd sourcing does not make it any better. Perhaps engaging a better local professional is the answer.

Here is the engineer’s drawing.

Mark - I don’t disagree. This is a terrible spot we are in. I’m just the poor soul paying for this place - nobody seems to know what the heck to do.

That is a poor design by any account. Where's your architect? A structural engineer just makes it stand up. I commented on reddit what one course of action could be.

At the very least the slab should be sloped away from the house.

https://noblecompany.com/products/noble-deck and better support and design detailing are in order.