In real life with partners who live together, it basically is a marriage. It's not like people don't accept that as real nowadays- but I'll be curious if with Tynion's run (however brief), he really is treating it like a marriage with Selina living with him in the mansion and everything, like she was when they were engaged (it sounds like she probably is, esp with Alfred gone, and with that solicit saying that Bruce Wayne is no longer a playboy, etc).
Although...I'm guessing no one will ever address this, but I assume they're going to retcon the fact that everyone knows Selina Kyle is Catwoman? Because if Bruce Wayne and Selina Kyle are publicly together, then that means he's dating Catwoman and everyone knows that? And if everyone also knows that Batman and Catwoman are a couple, then, how exactly would it not be obvious that Bruce is Batman?