Is "I vowed to be a righteous person in every way" considered a binding vow (nadhr wajib) that, according to the majority of scholars, is not valid?

If you had a specific intention when making the vow, beyond merely performing the obligatory acts, then you are bound by what you intended. If you intended by your vow to perform something from the commendable acts (mustahabbat), then this vow is binding upon you, and expiation is not sufficient for you except in cases of inability to fulfill it. However, if you did not intend anything specific, then the lowest rank of righteousness is to perform the obligatory acts and abandon the forbidden ones. Such a vow falls under the category of a vow to perform an obligation (nadhr al-wajib), which is not binding.