Yes - wet bulb temperature is a measurement; but when people say 'wet bulb temperature' they are referring to when it is 100% relative humidity and your body's thermoregulation shits the bed because your sweat can't evaporate because the air is already full of water & you die a painful heat stroke death.

A 'feels like' temperature of 106 is hot and definitely excessive heat which should be avoided as much as possible (especially if you're part of a vulnerable population, like the elderly, disabled, and young children) - but it is not a wet-bulb temperature because the air is not saturated with water. You can still cool down with evaporation & your sweat on a 106 degree day in 45% humidity. That's like a wet bulb temperature of 80F.

FWIW the temps shown in the OP are not measured wet bulb temps and are instead the heat index (i.e. 'feels like). The wet bulb globe temp is like 80-85F like I said. You can get a good estimate of the actual wet bulb temp based on dew point & air temp using this calculator: https://www.weather.gov/epz/wxcalc_dewpoint (or like the basic 1/3 rule where you take Air Temp - Dew Point, divide that by 3, and subtract the result from the Air Temp.)