Can’t for the life of me get this frickin’ thing Depined so I can get my new connector in. To my understanding, you lift up on these pins I circled in green and pull the individual wires out as your lifting the pin, right? I’m probably wrong 😂 any help would be GREATLY appreciated.

 

No. You have to push down on the black plastic tab (impossible to see in your pic) that engages into the underside of each metal pin and prevents you from pulling them out. Pulling on the wire before depressing the tab will lock the tab and pin in place. So don’t do that.
You need either a very small (~1.0mm wide) flat bladed watchmaker's screwdriver, or a specialized de-pinning tool, slid under each pin at the base of your green circle, to contact the tongue, hold it down, then pull on the pins gently .
If you screw the plug up, (it looks like it's gone a few rounds already), go here for a new one!