Brand New Day is basically the Spider-Man reboot that follows One More Day. It doesn't really touch on the One More Day events, at least not at first, except that One More Day is a necessary precondition for Brand New Day to happen. Eventually they go into the in-universe version of events, which is a version of No Way Home (though more successful): after being beset by problems related to having revealed his secret identity, Peter asks Dr Strange to remove the memory of him being Spider-Man from everyone (except, it turns out, MJ). It actually succeeds extra well, at least for a while, which makes it impossible for people to whom Peter hasn't actively revealed himself to make the connection.
If you can ignore the bad taste caused by One More Day, Brand New Day and the storylines following it (eventually leading up to The Superior Spider-Man) are actually really good. It feels like a throwback to "the good old days", with mysterious villains, a reinvigorated supporting cast, and all that good stuff. It also leans very strongly on the science side of Spider-Man, avoiding the mysticism Straczynski dabbled in.
I think both Straczynski's and the follow-up team's Spider-Man are great, but they're not really compatible with one another.