Improving awkward wiring
The left-hand part of the Ethernet connection is commonly called a keystone jack or a keystone module. All brands look more-or-less the same, but (to my knowledge) there isn't any formal industry standardization on the dimensions. One can rest assured that Leviton jacks will fit nicely into Leviton brand wall plates, but a Leviton brand jack might not fit so well into an unbranded wall plate from Amazon (purely as an example -- I can't tell from the photo what brand of jack it is).

You can try a wall plate such as the one linked. There's a fair chance the existing jack will fit well enough. If it doesn't, you can try again with another brand of wall plate or buy a jack and plate that are known to work together and replace the existing jack.