Very very quick little update: the character rotation while on the ledge is fixed. Here's how it looks now:

https://drive.google.com/file/d/1ROx3v3VsOmVGeErvtExlMlKQQjcIFScA/view?usp=sharing

I went in the wrong direction about solving this problem, at first. I thought that the camera and the capsule are the only two components that are directly involved in this issue. Turns out I overlooked a tiny little detail: the player controller.

The player controller acts as a thread tying the two components. That's obvious. What wasn't obvious (at least to me) was that you [b]can[/b] snip this thread and tie it back again, contrary to what I believed before, like the "camera has to get bound to the capsule component" thing....it's still valid. But you can tinker with all variables in the FirstPersonCharacter panel. As such, I found out that there is a tick box for the Use Controller Pitch Yaw. Untick it and the camera moves independent from the player character. It was as simple as that.

Lesson: When you think you have all the variables you need to solve a problem, think again. And then again, and again until the solution clicks.