Most doctor’s offices have an after hours line that you can contact in an emergency. They mostly just tell you either that you’re all good and call back in the morning, or to go to an ER, but there’s also a whole industry built up on after hours answering services. I don’t believe I’ve ever been charged for an after hours phone call.
There are also 24/7 free standing ERs throughout the US. (freestanding meaning not attached to a hospital) It’s kind of a racket, but they’re the latest hotness because insurance will see it as an ER visit rather than a clinic visit. They’re generally staffed by one doctor on a 24 hour shift (so they sleep there) one nurse, one front desk employee, and maybe a tech for x-rays and labs. The primary expense is in setting up the location, because there are more requirements to be an ER, so you need more equipment. In exchange they charge like an ER and an average visit is several thousand dollars.
And then there’s minor emergency/urgent care clinics that are able to handle less serious things, but they look about the same so people often believe they’re in a minor emergency clinic, but really are in an ER.
I would imagine eventually there will be legislation stipulating some level of clarity between the two, but as it stands now several companies are basically in heavy expansion mode to try and establish as many ERs as possible.
There’s a lot of 24 hour options as it stands, I don’t think your primary care physicians are necessarily looking for a way to expand their hours even further.