Other than Bob's suggestions.. there is one other thing you can do.. with wireless security off.. set a fixed channel. You generally will find 8 or 9 a good choice. It is one that is valid in all countries. And tends to keep off the more crowded channel 1.
No luck with that.. then yes.. it is simply incompatible. It happens with quite a few IOT products. Unfortunately Apple has removed logging and so it is very difficult to find out exactly where the problem is.
The solution is a wireless router or AP. I usually go TP-Link for these but almost any brand is fine. A cheap end standard N wireless router even second hand is perfectly ok for this job. You can press into service even old modem routers since you do not need a WAN port. You need to configure it so it is working as pure AP.
Tell us if you need instructions to do that. It does need to link back to the Airport with ethernet or powerline adapters. However some TP-Link wireless routers offer universal repeater mode.. and they do in fact work with any brand.. ie universal really means universal.
If powerline works for you .. you can buy powerline type adapters with wireless on one end.. so need for a secondary AP.
One other comment to offer a minor correction.
An extender might work, but it will need to be a brand other than Apple, and the extender will need to be permanently wired back to the Apple router in order to function correctly.
You can buy universal repeaters. They do work even with Apple routers, so it is possible to do this purely by wireless. I have used cheap end wireless AP/repeater successfully with Airport Extreme to extend wireless. You cannot do it the other way around.. ie Apple routers cannot extend another brand.
The results will be much poorer than using wired connection whether direct ethernet or powerline adapters.
And more difficult to maintain, due to the way repeaters work.
