Is anyone else having the issue? Is there a solution to this? 

I've tried running OBS and the game as admin, and I've tried multiple settings with Game capture and Window capture, and nothing works. I have one monitor so Display capture isn't an option.

I'm running on OBS Studio version 23.0.2.

It probably has something to do with the way it's rendering/the RPG Maker MV version.
Normally game capture doesn't work, but window does. That's not the case here though.
What you can do instead is use display capture and resize the recording area (Hold inside the screen preview area and move then resize the rectangle. Hold ctrl while doing so for it to not snap to the edges).
Here's my settings working with the same OBS version

I can confirm that this will work, and that I couldn't get it to capture the window specifically either.