I spent over an hour on the phone with two different Apple techs on this issue (pairing my old Bluetooth items with my new iPhone 16 Pro) yesterday. It turns out it doesn’t have anything to do with your network settings.
Oddly enough, it has to do with the individual devices and their initial Bluetooth setup steps. I had three different Bluetooth speakers (a Sony, a Marshall Emberton, and a Bose), as well as three different pairs of earbuds (a pair of Sonys and two pairs of craptastic knockoffs) that wouldn’t pair with my new iPhone, even though my Apple Watch and car had no problem doing so.
I was certain it just had to be the phone and not the SIX different Bluetooth items, but when the first Apple guy couldn’t figure it out, his supervisor came on, asked me the model # of each of the items I couldn’t pair, looked up the pairing instructions, &, amazingly, one by one, each one paired with my new phone when I followed his directions!
Now, I’m no tech newbie, and I had no trouble pairing any of this stuff the first time around with my iPhone 13. I also know I hadn’t followed the detailed steps he read off to me, either — even though I was reading along to a copy of the manual he’d sent me, so I know he wasn’t making this stuff up!
So try following the pairing steps of your Bluetooth device precisely from the manual, even though you’ve never had to do that before. Apparently the iPhone 16’s a prissy little thing that wouldn’t think of accepting an invitation from a Bluetooth device unless she was introduced properly through a formal courtship in the front parlor.