First, it's important to realize that there are many shades of Stoicism and many shades of free will. Within Christianity, the relevant topics are divine foreknowledge, divine plan, moral responsibility, grace, sin, and election, all of which need to be harmonized one way or the other. So it's no wonder that different traditions will harmonize them differently, and even for a single tradition like Lutheranism, a single work like Luther's "Bondage of the Will" may emphasize different aspect of free will than later formulation of the Lutheran position (such as the Formula of Concord).
The Stoic position as defined in the Formula of Concord you quoted has to do with determinism that excludes free will which most Christians cannot accept because it excludes moral responsibility.
But Martin Luther in his "Bondage of the Will" was responding to Erasmus's understanding of free will vs. divine foreknowledge which had nothing to do with Stoicism where divine foreknowledge is not a factor. So comparing the two is like comparing apple to orange.
Within Christianity there are different ways to balance affirming both free will and divine foreknowledge, so it's understandable that Luther disagreed with Erasmus. The language "necessity of consequence" has to do with describing the relationship, which has to be distinguished with "necessity of consequent" described in the 2014 Oxford Handbook of Martin Luther's Theology, Chapter II (Luther as Late Medieval Theologian), Section IV (De Servo Arbitrio), pages 40 to 42. This is a distinction maintained by the Scholastics (including Erasmus, I think) but denied by Luther (emphasis mine):
Luther closely connects his distinction with the problem of 'whether God foreknows anything contingently, and whether we do everything of necessity'. In doing so, he takes up a problem that was discussed by scholastic theologians and philosophers for centuries. God is omniscient, he cannot be deceived, his knowledge is immutable, and since he is a necessary being, his knowledge is necessary, too. Nevertheless, the problem is whether God who knows all and everything knows contingent entities and events as contingent or whether the necessity that he knows everything has the consequence that everything he knows is itself necessary. In this case, free will would not exist. Scholastic theologians made many and very different attempts to avoid this consequence and demonstrate that God's necessary knowledge is compatible with the contingency of the created world and with free will. Luther in fact broke with this tradition arguing: (a) God's will is immutable: thus his foreknowledge is immutable, too, and (b) if his foreknowledge is immutable, then 'God foreknows necessarily'
In another work discussing this issue, from 2018 book Luther's Outlaw God: Volume 1: Hiddenness, Evil, and Predestination:
Consequence means God does something but consequent means God refrains from doing anything. Both are done in order to make God's eternal law the deciding factor in human lives.
It can be argued that Luther, in the heat of rhetoric, went too far (see Introduction of a translation of "On the Bondage of the Will"):
Erasmus had found a way of dissociating himself from Luther without in any way repudiating that concern for reform which they shared in common. He could take issue with him on a point of doctrine, concerning divine grace and human freedom, on which he differed from him totally. For Luther in his Assertio, 9 published in 1520, had utterly denied the reality of human freedom and asserted that everything that happens, happens by absolute necessity.10 This was in fiat contradiction to the teaching of the church, which, however much room it had left for debate about its extent and efficacy, had always maintained the reality of human freedom. Here Luther was wrong; and he was wrong, not only in what he taught, but in publicizing it; for it could not but have effects deleterious to any reform—it provided the common herd with a perfect excuse for every kind of wickedness and ungodliness.
In a summary of Luther's Bondage of the Will the author also warns us that "necessarily does not mean compulsorily":
I could wish, indeed, that a better term was available for our discussion than the accepted one, necessity, which cannot accurately be used of either man's will or God's. Its meaning is too harsh, and foreign to the subject; for it suggests some sort of compulsion, and something that is against one's will, which is no part of the view under debate. This will, whether it be God's or man's does what it does, good or bad, under no compulsion, but just as it wants or pleases, as if totally free.
Therefore, to properly interpret what Luther meant by "free will" it's very important to realize that in that work Luther focused on how we cannot have faith in Jesus apart from 100% God's grace, a kind of predestination, although different than the Calvinist flavor, as argued in a First Things magazine article by a Lutheran.
Therefore, the discussion of "necessity of consequence" in that work does not mean Luther abandoned free will totally, but has to be interpreted in light of divine foreknowledge of how certain humans (like Judas) will sin while maintaining Judas's "real" freedom to sin. There is already a fine answer to a related question by Mike which tried to show how even within "Bondage of the Will" Luther still affirms free will, although it's free will to sin.
Luther's position in that work I think harmonizes well with the conclusion of the Formula of Concord Section II (Free Will), 3rd Affirmative Thesis:
With these brief words He denies to the free will its powers, and ascribes everything to God's grace, in order that no one may boast before God.
It's important to remember that philosophical discussion of free will within moral philosophy (i.e. human agency) should be distinguished from theological discussion of free will within theology (where human will is corrupted by sin). A good background and contrast can be found in Chapter 6: The Protestant Reformation of The Cambridge History of Moral Philosophy
Personal assessment (not necessarily the Lutheran position)
Luther rightly points out the danger, especially when we were not yet regenerated, that our free will is in bondage and in desperate need of God's grace, especially in coming to Jesus to be born again (where we need God's grace 100%, so we cannot boast). While Luther may have gone too far in linking God's foreknowledge to human action (which I think could make God a party to our sinful actions), as regenerate Christians currently undergoing sanctification we should have a daily reminder that:
Our "free will" is still under the dark spell of evil tainting our desires and thus corrupting our reason which has the role to inform the will. Therefore we still need a daily dose of God's grace to counter it, making us humble before God
Just because God has the foreknowledge of our sinful actions, we cannot waive responsibility and give up either, because God truly wants us healed, and I think the healing will culminates in the total recovery of our free will, if not on earth, but for sure in the new creation after the day of judgment.
