I think you're misunderstanding what's going on in this passage. The "freedom" Heidegger speaks of here isn't what I understand by "freedom" in a particularly political sense (at least not in the first instance). Heidegger's use of the word "freedom" here derives from the conversations in German philosophy of his time. Pertinent to this is Schelling's Philosophical Investigations into the Essence of Human Freedom, where Schelling writes that "free is what acts only in accord with the laws of its own being and is determined by nothing else either in or outside itself." Freedom, in this sense, is the capacity to be what one is.
A key to understanding what Heidegger means by freedom is in §40 (p. 182), where he writes:
Anxiety reveals in Dasein its being toward its ownmost potentiality
of being, that is, being free for the freedom of choosing and grasping itself. Anxiety brings Dasein before its being free for ... (propensio in) the authenticity of its being as possibility which it always already is.
Freedom [Freiheit] here isn't a goal, its more precisely a characteristic of Dasein that it always already is. The freedom in question is its freedom to choose and grasp itself [Sich-selbst-wählens und -ergreifens], i.e. to take itself up as it is. Hence, in the same passage he writes:
But, at the same time, it is this being to which Dasein as being-in-the-world is entrusted.
In short, the freedom at stake isn't "the power or right to act, speak, or think as one wants" (or something along those lines) but rather the freedom to be what one always already is. This freedom is the condition for the possibility of their being something like "authentic, existentially projected being-towards-death" at all. More precisely, this "freedom" is the condition of possibility of the authentic / inauthentic relationship that Dasein can have with itself. Thus, in §41 / p.185, he writes:
Being free for its ownmost potentiality-for-being, and thus for the possibility of authenticity and inauthenticity, shows itself in a primordial, elemental concretion in anxiety.
One can object that "freedom" isn't what is at stake here. Very well, but that's to use another conception of freedom from the one Heidegger develops throughout Being and Time.