Maybe you've heard about the gefühlte Temperatur, or in English the apparent temperature: The temperature that humans perceive can be different from the temperature objectively measured by a thermometer, depending on factors like wind speed or humidity.
Some years ago, that "gefühlte Temperatur" started to appear in weather reports. The report could for example say, "die Temperaturen morgen werden um 0° Celsius liegen, gefühlt um -2° Celsius". This means something along the lines of "tomorrow temperatures will be around 0° Celsius, which will feel like temperatures around -2° C".
From there, the phrase "gefühlt etwas" has been extended to other topics where the perceiption differs from reality. This is often quite tongue-in-cheeck, but may not be in other cases, especially when people give their perceiption more credit than reality. For example
Sie hing gefühlte zwei Stunden in der Telefon-Warteschleife fest.
She was stuck on hold for what felt like two hours.
Gefühlt an jeder Ecke macht doch jetzt ein Handy-Laden oder ein Nagelstudio auf.
It looks to me like every other newly opening store is either a cell phone store or a nail salon.
or, as a much less harmless example
Gefühlt kommen Millionen Asylanten ins Land, und wir Steuerzahler dürfen das finanzieren!
It looks to me like millions of asylum seekers stream into the country, and we tax-payers are the ones to pay for all of that!
You can probably see how this can get easily very dangerous.
In your example sentence
Man weiß halt gefühlt nichts.
this "gefühlt" gets applied to "nichts". So you don't know nothing, but what you know feels like nothing to you, or is perceived as nothing.