For DIY - this is also a placeholder.
No idea what the story behind this is. It's a single gang coax box, and just a hole next to it. Looks like previous owner started to patch the drywall by putting the backer in but gave up.
Depends on how much work you’re willing to put in. I think you’ll find matching that texture to be quite a big pain in the ass. So what I would do is make a faux secondary outlet and just cover-up the previous mistake By making it look by design.
I had to deal with this exact situation, installing the backer myself (those stirring sticks from the hardware store are choice when doubled).. getting the texture right is a righteous pita.
If I had to do this again, a cheat might be something like a two gang plate but one is blank:
Those blank combo plates are a lifesaver for weird situations lke this - Arlington makes a low voltage mounting bracket that would work perfectly with that hole size too without needing to match texture.