Like I said, these exist. Not necessarily with SmartThings integration though. There are most all called RF (for radiofrequency) devices which send a signal to a nearby receiver. It might be your phone, it might be some kind of plug-in Bridge Device. The typical range is 3 m, but some of them are even shorter.
Most of them are designed to unlock a dog door, which is what most of the project reports on the link that I gave you are talking about. Take a look at those, and you’ll see some of the possibilities.
A lot depends on the exact details of what kind of notification do you want to get. Is it only for people who are in the home at that time? Do they all have android phones? Do you need smartthings integration or not?
Also, How much do you want to spend? You have to deal with both the cost of the tag itself and the receiving station for it. If you’re willing to spend, say, $150 you would have several choices. If you want to spend $100 they would still be a couple. If you want to spend under $50, it’s going to get more complicated.
But just as one example, you could use a radius network RadBeacon chip, which costs about $10, and Probably get notifications on android phones at your home, it’s just going to depend on the architecture as to whether you would have full coverage there. You would probably need to add Aa $20 Wi-Fi phone to detect it. (If you want to integrate with SmartThings you’re going to have to start adding at least some third-party apps for another $20 or more.)
Also, some people build their own receiving stations with an Arduino, so that would lower the cost but is obviously much more complex.
Probably not for your house, but included for completeness
Still Another option is a pressure mat that the dog steps onto naturally. For example, these are often used as doorbells for houseboats, but in the past community members have use them at Halloween for special effects, or as a sensor to report that someone is sitting on a couch. They wouldn’t require any special training. The only issue with these is that they will report any time a human steps on them as well, so I understand it may not be what you want. Also the dog might like it too much, and take to sleeping on the mat, that can happen. But I just mention it for completeness. They can be popular for knowing when the dog is ready to come in from the yard. 