Im not sure Ledger support can help you here. It sounds like it was your fault (I dont mean to be judgmental). It is surprising to hear that someone with your experience could have fallen victim to a phishing scam.
Since it was from their app, it wasn't a phishing scam. For some reason, their app is connected to their scam page. And trust me, experience isn't the issue here. In the crypto space, you can easily get "hacked" from somebody/ something...
It sounds like it was from the blockchain, not the Ledger app. If someone sends you an NFT with a link to claim it....kind of suspicious, no? This happens a lot, sorry it happened to you. You probably authorized the webpage to take your coins.