Main Entry: free·dom
Function: noun
1 : the quality or state of being free: as a : the absence of necessity, coercion, or constraint in choice or action b : liberation from slavery or restraint or from the power of another c : the quality or state of being exempt or released from something onerous
2 a : a political or civil right b : FRANCHISE 2
So:
The absence of ... coercion to support a state religion with which one disagrees.
the quality or state of being exempt ... from something onerous like supporting a state religion with which one disagrees.
The "no establishment" clause protects a freedom (from a state religion).
Your foray to the dictionary ios admirable, but misguided. For it cannot help you in this instance. Your confusion is similar to many people’s over “substantive” due process. That is, you confuse something which leads to freedom with freedom itself. Non-establishment is not a freedom, though it does leave you free from state religion.