I'm pretty sure the OMNY Card is essentially a sturdier Metrocard with an NFC chip instead of a magnetic stripe that you can top up either online or at a vending machine, not an account like a credit or debit card that you can load into Apple Wallet.

If you want to use Applepay without individual rides cluttering your main credit card statement, you could set your Express Transit Card to an account you don't use for anything else. You could use a dedicated credit card (Citi Custom Cash would be a good choice for this with no annual fee and 5% cash back on the first $500/mo in your top spending category and reliable autopay that pulls the statement balance from your bank each month) or Apple Cash (although you can only load it from a debit card, so no rewards). There are also some credit cards (I think Chase Ink business cards, for one?) that have different card numbers for different authorized users and segregate the charges on the statement by user, so if you have a family member who isn't already an authorized user you could probably make them an AU and add their card to your Apple Wallet for transit.