This port is in the Mediterranean, not the Red Sea. And no, wheels have not been found. One of the crockumentary makers had a brass wheel made to take some footage of a chariot wheel on the bottom; there’s also some modern machinery from 19th- and 20- century wrecks and things. No chariots.
I saw a site that showed what looked like wheels.
Many of them have gracefully-curved spokes and/or are "faired" (with spoke ends flared out and blended into the wheel and hub). AFAIK, no ancient wheelwright ever did either of those things; it would simply be too much work for no functional improvement.
Now, if you want to see the exact same things -- out of the water -- go to Google Images and search for "valve wheel". You will be greeted with a page of pictures of wheels that look exactly like those depicted underwater -- complete with curved spokes and "faired" spokes.
Note that many of the similar valve wheels have square or hexagonal holes in the center. It is common for the worker to carry a wheel with him from valve to valve, slip the wheel over the square or hex valve stem, adjust the valve, remove the wheel -- and carry it with him to the next valve.
Unsurprisingly, valve wheels occasionally get dropped overboard or are washed or roll overboard when dropped.
Conclusion: those "chariot wheels" are merely modern valve wheels that fell overboard from tanker ships.
Don't feel bad -- those "sunken chariot wheels" had me wondering at first, too... '-)
Texas Archaeological Steward