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As of now, Mbed OS does not have support for WPA3 personal security. There is an ongoing effort to add support in the mbed-os\features\netsocket\emac-drivers\TARGET_Cypress\COMPONENT_WHD\interface\WhdSTAInterface.cpp. But I can't provide you with an exact timeline of this feature, to be merged with mainline mbed-os release.
As of now, you can use WICED Studio to test out this feature which has WPA3 support integrated in the 6.4 release. But as feature wise, WPA3 personal security is supported in WHD and the WLAN firmware for CYW4343W also has support for WPA3 but the mbed os SDK does not have provision for WPA3 yet.