How can I install a TV mount to metal studs?

Yes. It looks like metal studs. You can use a piece of plywood just smaller than the TV on the wall and mounted to the studs to help distribute the weight. I've mounted a few like that.

A few things to consider when mounting is the weight of the television and whether it is a flat mount or swivel. If the TV is heavy or on a swivel mount the "right" way to do it would be to open the wall and use wood studs to build a good support.

Here's my thoughts on metal stud mounting, but my preferred method is below this:

If the TV is not too heavy, I've mounted to metal studs using toggle bolts. 3/16" if its on the lighter side, 1/4" if heavier. The pilot hole for a 1/4" toggle bolt needs to be 5/8" so its important find the center of the stud. This means finding the location where it starts and ends and drilling as close to center as possible. You can use a stud finder to mark the approximate edges and then use the smallest drill bit you have to drill inside the markings to confirm where the edge is. Measure and mark the center. When you drill, take it slow, and have a sharp bit that can drill metal. After you drill through the drywall pull the bit out to clear the dust, then start drilling the stud with some pressure but not so much you bend it. This might pop the other screws on the stud above and below the area you're drilling. Let the drill do the work, once it catches the metal and punches through it might be rough because the drill bit edges will catch the stud and rattle it. Then setup your anchor bolts on your mount and push them all through and let the frame hang before tightening. You may have to fiddle with the bolts to make the backs flip up and down.

The other, and my preferred option if the wall is standard drywall and the tv/mount is not too heavy is to mount directly to the drywall using the name brand Snaptoggle Toggler bolts, they work great. The exact weight tolerances are here: https://toggler.com/pdfs/SNAPTOGGLE%C2%AE-Heavy-Duty-Toggle-Bolts.pdf but I recommend erring on the side of caution. Buy a couple extra because the snap off feature can sometimes be tricky to get a hang of.