We figured out Apple's technical support, as it turned out, this and possibly series S | X do not work directly, but through the Mac os API, which means that half of the software sees it only after adding it to "Settings -> security -> input monitoring". And the other part of the software compiled without API support does not see it at all. There is no such problem with the Xbox one gamepad, the one in the photo. Left a bug report with apple about this.
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