Phoenix have the same function but are more discreet about it.

So they know all your channel and the final recipient of all ur coins.

and when u close those channel w them the know the onchain wallet.

Breez doesnt talk at all about it but its lightning so its like other LN wallet.

So if i summerize in general in LN the wallet provider record all u do.

I still search about why WOS and not the other wallet. Maybe i miss some connected people ?