I feel for you. Its probably saddening to see quality degrade over time.

I would say this is a values mismatch, if the client does not care about prioritizing technical debt(no matter how it got created) and that is leading to too much mental angst, I would recommend leaving the project. But before you make that decision, think about what you said

"They still want me to participate in the project and work on the most critical parts of the application"

I think in this new world, the job of software engineering is to identify where AI could be used to provide the highest levers to the most important people in the client's team to make decisions. For example, can AI be used to identify problems quickly and troubleshoot them? Can it be used to provide APIs or with better observability(e.g. quantify that the system performance coming down is not sustainable)?

Another thing that is weird about this is the human aspect. Specifically role of the product manager. Ideally he should be someone who is experienced enough and acts as a moderator between what code/features go in and what don't. The client always wants the moon and a good PM's other real job is to manage this friction. Is he not able to push back? He is also the one that is looking at the project timeline and making such decisions. If that role is not being played by someone, then something is obviously wrong with the relationship.

I've had project that tried a similar thing, they tried to replace their team with cheaper coders. They went slower because of code slop and their product failed to launch on time and be successful.