If you are in the US, many models will be illegal in many jurisdictions unless you put the sensor outside so that it can only hear what anyone walking past would hear.
There is an expectation of privacy inside of a rental and the landlord is not allowed to listen into activity, which is what this could entail. Even if it’s only the noise level, that covered by privacy laws in some jurisdictions. But more and more places are allowing for noise level monitoring for exactly the reason you give, to prevent loud parties. So as long as it only reports above the local “nuisance“ level and doesn’t record anything, you’re probably OK. You just need to check the details.
Also check the vacation rental broker if you use one, because they will also have rules about acoustic monitoring.
But again in most jurisdictions, you would be fine with one in the yard. Or one that is specific to nuisance level noises.
OK, having said all that, there are several existing threads on this topic. I think the following is the most recent.
Zwave or zigbee sound detectors
As you noted, Airbnb does itself recommend the specific brands you listed, but I think all of them are set to only report above the nuisance level. 
and as you also noted, they have subscription fees and there’s no direct integration with Smartthings. You might be able to do something on an android phone by capturing a notification, but of course that doesn’t get around the subscription cost.