There are different brands and types of extenders. Some of the hoses have actuators as seen in your example and others are holding the tire pressure so there is no actuator issues.
In my experience the biggest problem with extenders is that the outer end is not always locked down hard so there is excessive flex which can cause leaks or early failure. This is my set-up for the past 7 years and 27,409 miles with no failures or leaks. These steel braided hoses are the pressurized type. NOTE this picture does not show my external TPMS.
I also have to comment on the use of rubber valve stems. This is definitely the fault of the company that mounted the tires and if Forest River accepted the tire & wheel assembly with less than the tire max inflation then they are at fault for this unsafe practice. Rubber snap in stems are rated 65 psi MAX and should NEVER have been used in an application that used LR-D or LR-E tires and isn't a good plan even for LR-C tires.
I write a blog on RV tire application and safety. RVTireSafety.com
Also give seminars on tires at RV events across the US. 40 years experience as tire design & quality engineer for major tire mfg. Freelander 23QB on Chevy chassis is my RV