After a few tests with various Android Auto/Carplays wireless adapters, I found this one that fits completely in the USB socket and allows the cover to be put back in place. It will not completely close (I didn't dare to push it too hard), but the cover doesn't move and resisted washing the bike:

https://nl.aliexpress.com/item/1005010194152550.html?spm=a2g0o.order_list.order_list_main.95.7bd15e5bZZEKvm&gatewayAdapt=glo2nld