Apple Pay on the Web requires my phone and email. Is that information shared?
Only being asked these details while on a Mac enabled me to use desktop Safari's Network Inspector, and actually see what's being sent to the server.

When prompted, I couldn't choose an existing contact, so I had to create a new one (but it wasn't added to my Contacts either, even though the payment went through). Lets say I used John Doe with +1 (505) 842-5662 and myemail@example.com.

The request was sent to https://ticket-shop.example.com/api/v3/payment/applepay/fast-checkout with the following data:

{
    "paymentData":{
        "paymentData":{
            "version":"EC_v1",
            "data":"SOME_BASE64_LOOKING_STRING",
            "signature":"SOME_BASE64_LOOKING_STRING",
            "header":{
                "ephemeralPublicKey":"SOME_BASE64_LOOKING_STRING",
                "transactionId":"SOME_HASH"
            }
        },
        "paymentMethod":{
            "displayName":"MasterCard 1234",
            "network":"MasterCard",
            "type":"debit"
        },
        "transactionIdentifier":"SOME_HASH"
    },
    "eventAlias":"example-standup",
    "consumerContact":{
        "emailAddress":"myemail@example.com",
        "familyName":"Doe",
        "givenName":"John",
        "phoneNumber":"+1 (505) 842-5662",
        "phoneticFamilyName":"",
        "phoneticGivenName":""
    },
    "_csrf-frontend":"SOME_BASE64_LOOKING_STRING"
}


So Apple Pay did share that information with the merchant. Moreover, in a confirmation e-mail I received from them, they used the test name I entered while paying, not the name they have on file for me. 

So apparently some merchants will request this additional info, while others don't. I couldn't find any official sources, so this is merely an observation that didn't fit into a comment, and not an answer.