you could add slim cabinets/storage towers on either side of the FP for all your stash needs

neaten up the area and the TV won't look so high.

Can they be next to the fireplace or do they need to be up there? Either way, you can dump them in a nice basket or decorative box. Cut holes where needed. Do some cable management with clip or something so they lay flat and wrap tightly around corners.

What about making a boxy thing under the TV over the entire shelf? Like a 3-sided screen, 4-5" tall or whatever fits under the TV. Make it from molding, paint to match the mantel.

Pretty fireplace.

https://www.huffpost.com/entry/how-to-hide-unsightly-computer-cords-cables-on-your-desk_l_5f4524efc5b6c00d03b46245

Something like this (this one is from CB2)

put it on the left side of your fireplace. Take off the back of it

Lets see the whole space . My advice get the darn TV off the mantel find a wall get a nice low cabinet mount the TV so the cords are hidden and all the rest go in the cabinet

I’d love to take the tv away from the fireplace but I lost that battle.

How about some nice satin cord covers? I'm not sure if I'm serious or not. Doesn't take care of the big pieces of course. But the power strip can be nailed to the wall behind the TV and the router stuff...

Can you pull the TV down and forward and just shove all that junk behind it?

Hire an AV professional to put the equipment in a closet and the wires in the wall .

If you have a wireless router - and I would be surprised if you don't - it doesn't need to be in the same room with the TV. Ours is in a closet in the middle of the house. Have you looked to see if a smaller surge protector is available?

Can you run the cables through the wall and put the boxes/router in the workout room behind the fireplace?

There is a verizon modem and then a wireless router plugged into that on the mantle to the left of the TV, all the wires come up from the left side near the floor including the power strip. All that could easily be on a table next to a fireplace, there is no reason all that needs to be where it is. The TV is older and probably not a smart TV on top of that. A little device like Roku could update it and make it wireless.