The operative word translated "firmament" is רָקִיעַ (raqia) which is variously translated, "expanse", "space", "vault", "dome", etc.
BDB defines the word as "extended surface, (solid) expanse (as if beaten out; compare Job 37:18)".
In any case, this "firmamemnt" is that which exists between the waters below (livers, lakes, seas, etc) and the waters above (the source of the waters below, rain clouds, etc). In modern parlance, we might call this either "atmosphere" or "sky". (Clearly, it is not outer space!)
The OP quoted text then defines this "firmament" as "heaven" or "sky" (in some versions) and this same word is used to describe the place where birds fly, Gen 1:26, 28, 30, 2:19, 20, 7:3, 23, etc.
Thus, there is no doubt that "firmament" is the place where birds fly and the space between the waters above and below, ie, what we now call sky/atmosphere.
