I have not visited bitcoin.org (nor bitcoincore.org) for a very long time therefore have no idea what wallets they are recommending. Having said that, what can be stated about Ginger Wallet is that they charge a fee and they do not allow for users to enter their coordinator. If you use Ginger Wallet you have no choice but to use their coordinator.
Wasabi Wallet does allow users to enter a coordinator of their choice (including those that charge 0% fees). On that basis, it becomes an almost pointless exercise to use or recommend Ginger Wallet.
These days I visited the bitcoin.org site, and in the recommended wallets, I saw the ginger wallet listed as one of the options for desktop wallets/software wallets, this is a worthy recognition and they should probably be doing a great work.
I don't know how the wallet is currently, but it would be interesting, if it doesn't already exist, to add fee under 1 sat/vB (like 0.1, 0.5 sat/vB) and full support for silent payments.