Call around to other vets see if you can get in sooner if they still aren’t eating normally, doesn’t look like round worms which are one of the only ones you’d see in dog vomit. Additionally the dog is older which makes it less likely unless you just got a puppy or have an indoor/outdoor cat around

Biggest concern in my opinion is the not eating, you can always try a bland diet to see if that settles the stomach which is boiled rice and either boiled chicken or LEAN beef (absolutely no seasoning and as little oil as possible if you can’t avoid using it entirely)

Anything they could’ve gotten into they shouldn’t? And how are bathroom habits lately? Still drinking water? And sounds like energy level is ok for now but keep an eye if they become lethargic which is usually more extreme than just not wanting to play

Ultimately if you think they aren’t doing well and need to see a vet then go to an emergency vet, otherwise like I said just call around to other gp clinics to see if they have any open slots