How can I hide these cords safely?

Buy a cord organizer. It is a plastic tube slit lengthwise. Shove cords into sleeve.

I used a hint from this site and purchased a small plastic solid basket at Dollar Tree, put it under my desk and put the surge protector and its many plugged-in cords in the basket. Works great and makes it easy to clean under there. I did have to cut out a section of the basket to accommodate the protector's large cord since there was a piece of board across the back (what used to be called a "modesty shield" -- it screened a lady's legs from passersby).

Besides putting a box or basket over them you can’t hide them effectively. Oh you could shorten them by purchasing replacement plugs from a hardware store or big box store and cutting the cords to the shortest length possible but be sure to get a replacement plug that fits the shape of the cord you are replacing, i.e. flat slot in the replacement plug housing, or round hole. However if you take this route you will have very short cords and they probably won’t be Long enough to use elseware. Also the picture shows a really long cord that is closely coiled together. This is not good. It can create an electrical coil that could build heat. If it is just a telephone wire go to a store like Best Buy and buy a shorter cord.

For my mounted tv I bought a neoprene sleeve that has Velcro to wrap around the cords. That will keep them bundled into one group but also I used it to wrap around the telescoping arm of the mount. They make tubes with slits, or just Velcro straps or twist tie type things to organize the cords. Then, Bbunny had a great idea in going to the dollar store for a cheap basket. I bought a black plastic container that has slots on the side and a lid off Amazon for mine.(and it cost a lot more than a dollar!) A basket would probably have worked but since I’d be mounting it behind the tv, and we are considering selling the house, I wanted it to look as professional as possible. I’m not done with the project but I’m attaching a pic. I measured the bracket on the tv, came up with a couple nuts and bolts, then drilled holes in my container like a keyhole shape so I could pre-attach the nut/bolt loosely then just tighten once the box was successfully hung onto the bolts. If you wanted to get that multi port off the ground you could do something similar if there is something to hang the basket (or box) onto.

Imade a curtain to match the roomdecor and hung it in the back of the desk knee hole with a tension rod and walah no moer visible computor cords Easy to remove and clean behind when necessary

Tape paper towel tubes together, paint them, cover them (whatever matches your decor) and slit them, shove the cords in! Done!

Swimming noodles about the same color, split length wise. Run the wires through the noodles, make a small note on it if you need to keep track of which appliance the wire are for, good to go!