Although I don't have a complete answer this question is special, the difference from the common "how do I test" questions is the high frequency of changes. Testing everything thoroughly is one approach, but as @vicky99 explained it's not worth investment for a very short lived feature.
There two approaches to go as I see it. One approach that could help, but highly depends on your product, is having a good test infrastructure- environment, test runner, test API, test framework, documentation for those etc. and then try moving testing to the left towards the developers and early in the development stages.
Having a solid test infrastructure means that a developer can add tests relatively quickly and painlessly, those test might be rudimentary but that's better than having none at all. The test automation specialist of the team will support this effort by maintaining the test infrastructure and adding to it new features in parallel to development of new features.
Up to here this sounds like a normal way a team should work but you must adapt it for speed and efficiency, for example by even better communication between developers, putting test development higher in priority or accepting simpler tests first and only later improving them.
The other approach, which might not stand on it's own, is having excellent monitoring and data analysis. Since you already have AB testing you probably have telemetry being sent back and analyzed. You can use this data to test in production and look for bugs, you should probably have an automated system analyzing the data raising alarms and you should make this system smart looking not only for error reports but also for abnormal usage patterns for example. Since you already have basic testing done using the above approach you can be pretty confident that your features are stable and bugs won't be too common.